TSTP Solution File: SET641+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET641+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 05:07:28 EDT 2022
% Result : Theorem 1.33s 1.09s
% Output : Proof 1.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET641+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 07:18:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 1.33/1.09 % SZS status Theorem
% 1.33/1.09 % SZS output start Proof
% 1.33/1.09 tff(member_type, type, (
% 1.33/1.09 member: ( $i * $i ) > $o)).
% 1.33/1.09 tff(tptp_fun_B_10_type, type, (
% 1.33/1.09 tptp_fun_B_10: $i)).
% 1.33/1.09 tff(tptp_fun_D_3_type, type, (
% 1.33/1.09 tptp_fun_D_3: ( $i * $i ) > $i)).
% 1.33/1.09 tff(cross_product_type, type, (
% 1.33/1.09 cross_product: ( $i * $i ) > $i)).
% 1.33/1.09 tff(tptp_fun_D_12_type, type, (
% 1.33/1.09 tptp_fun_D_12: $i)).
% 1.33/1.09 tff(tptp_fun_C_11_type, type, (
% 1.33/1.09 tptp_fun_C_11: $i)).
% 1.33/1.09 tff(ilf_type_type, type, (
% 1.33/1.09 ilf_type: ( $i * $i ) > $o)).
% 1.33/1.09 tff(set_type_type, type, (
% 1.33/1.09 set_type: $i)).
% 1.33/1.09 tff(power_set_type, type, (
% 1.33/1.09 power_set: $i > $i)).
% 1.33/1.09 tff(subset_type, type, (
% 1.33/1.09 subset: ( $i * $i ) > $o)).
% 1.33/1.09 tff(relation_type_type, type, (
% 1.33/1.09 relation_type: ( $i * $i ) > $i)).
% 1.33/1.09 tff(member_type_type, type, (
% 1.33/1.09 member_type: $i > $i)).
% 1.33/1.09 tff(empty_type, type, (
% 1.33/1.09 empty: $i > $o)).
% 1.33/1.09 tff(subset_type_type, type, (
% 1.33/1.09 subset_type: $i > $i)).
% 1.33/1.09 tff(1,plain,
% 1.33/1.09 ((ilf_type(B!10, set_type) & (ilf_type(C!11, set_type) & (~(ilf_type(B!10, relation_type(C!11, D!12)) | (~ilf_type(D!12, set_type)) | (~subset(B!10, cross_product(C!11, D!12))))))) <=> (ilf_type(B!10, set_type) & ilf_type(C!11, set_type) & (~(ilf_type(B!10, relation_type(C!11, D!12)) | (~ilf_type(D!12, set_type)) | (~subset(B!10, cross_product(C!11, D!12))))))),
% 1.33/1.09 inference(rewrite,[status(thm)],[])).
% 1.33/1.09 tff(2,plain,
% 1.33/1.09 (((~(~ilf_type(C!11, set_type))) & (~(ilf_type(B!10, relation_type(C!11, D!12)) | (~ilf_type(D!12, set_type)) | (~subset(B!10, cross_product(C!11, D!12)))))) <=> (ilf_type(C!11, set_type) & (~(ilf_type(B!10, relation_type(C!11, D!12)) | (~ilf_type(D!12, set_type)) | (~subset(B!10, cross_product(C!11, D!12))))))),
% 1.33/1.09 inference(rewrite,[status(thm)],[])).
% 1.33/1.09 tff(3,plain,
% 1.33/1.09 ((~(~ilf_type(B!10, set_type))) <=> ilf_type(B!10, set_type)),
% 1.33/1.09 inference(rewrite,[status(thm)],[])).
% 1.33/1.09 tff(4,plain,
% 1.33/1.09 (((~(~ilf_type(B!10, set_type))) & ((~(~ilf_type(C!11, set_type))) & (~(ilf_type(B!10, relation_type(C!11, D!12)) | (~ilf_type(D!12, set_type)) | (~subset(B!10, cross_product(C!11, D!12))))))) <=> (ilf_type(B!10, set_type) & (ilf_type(C!11, set_type) & (~(ilf_type(B!10, relation_type(C!11, D!12)) | (~ilf_type(D!12, set_type)) | (~subset(B!10, cross_product(C!11, D!12)))))))),
% 1.33/1.09 inference(monotonicity,[status(thm)],[3, 2])).
% 1.33/1.09 tff(5,plain,
% 1.33/1.09 (((~(~ilf_type(B!10, set_type))) & ((~(~ilf_type(C!11, set_type))) & (~(ilf_type(B!10, relation_type(C!11, D!12)) | (~ilf_type(D!12, set_type)) | (~subset(B!10, cross_product(C!11, D!12))))))) <=> (ilf_type(B!10, set_type) & ilf_type(C!11, set_type) & (~(ilf_type(B!10, relation_type(C!11, D!12)) | (~ilf_type(D!12, set_type)) | (~subset(B!10, cross_product(C!11, D!12))))))),
% 1.33/1.09 inference(transitivity,[status(thm)],[4, 1])).
% 1.33/1.09 tff(6,plain,
% 1.33/1.09 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~ilf_type(D, set_type)) | (~subset(B, cross_product(C, D))))))) <=> (~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~ilf_type(D, set_type)) | (~subset(B, cross_product(C, D)))))))),
% 1.33/1.09 inference(rewrite,[status(thm)],[])).
% 1.33/1.09 tff(7,plain,
% 1.33/1.09 ((~![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => ![D: $i] : (ilf_type(D, set_type) => (subset(B, cross_product(C, D)) => ilf_type(B, relation_type(C, D))))))) <=> (~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~ilf_type(D, set_type)) | (~subset(B, cross_product(C, D)))))))),
% 1.33/1.09 inference(rewrite,[status(thm)],[])).
% 1.33/1.09 tff(8,axiom,(~![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => ![D: $i] : (ilf_type(D, set_type) => (subset(B, cross_product(C, D)) => ilf_type(B, relation_type(C, D))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_relset_1_3')).
% 1.33/1.09 tff(9,plain,
% 1.33/1.09 (~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~ilf_type(D, set_type)) | (~subset(B, cross_product(C, D))))))),
% 1.33/1.09 inference(modus_ponens,[status(thm)],[8, 7])).
% 1.33/1.09 tff(10,plain,
% 1.33/1.09 (~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~ilf_type(D, set_type)) | (~subset(B, cross_product(C, D))))))),
% 1.33/1.09 inference(modus_ponens,[status(thm)],[9, 6])).
% 1.33/1.09 tff(11,plain,
% 1.33/1.09 (~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~ilf_type(D, set_type)) | (~subset(B, cross_product(C, D))))))),
% 1.33/1.09 inference(modus_ponens,[status(thm)],[10, 6])).
% 1.33/1.09 tff(12,plain,
% 1.33/1.09 (~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~ilf_type(D, set_type)) | (~subset(B, cross_product(C, D))))))),
% 1.33/1.09 inference(modus_ponens,[status(thm)],[11, 6])).
% 1.33/1.09 tff(13,plain,
% 1.33/1.09 (~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~ilf_type(D, set_type)) | (~subset(B, cross_product(C, D))))))),
% 1.33/1.09 inference(modus_ponens,[status(thm)],[12, 6])).
% 1.33/1.09 tff(14,plain,
% 1.33/1.09 (~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~ilf_type(D, set_type)) | (~subset(B, cross_product(C, D))))))),
% 1.33/1.09 inference(modus_ponens,[status(thm)],[13, 6])).
% 1.33/1.09 tff(15,plain,
% 1.33/1.09 (~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ![D: $i] : (ilf_type(B, relation_type(C, D)) | (~ilf_type(D, set_type)) | (~subset(B, cross_product(C, D))))))),
% 1.33/1.09 inference(modus_ponens,[status(thm)],[14, 6])).
% 1.33/1.09 tff(16,plain,
% 1.33/1.09 (ilf_type(B!10, set_type) & ilf_type(C!11, set_type) & (~(ilf_type(B!10, relation_type(C!11, D!12)) | (~ilf_type(D!12, set_type)) | (~subset(B!10, cross_product(C!11, D!12)))))),
% 1.33/1.09 inference(modus_ponens,[status(thm)],[15, 5])).
% 1.33/1.09 tff(17,plain,
% 1.33/1.09 (ilf_type(C!11, set_type)),
% 1.33/1.09 inference(and_elim,[status(thm)],[16])).
% 1.33/1.09 tff(18,plain,
% 1.33/1.09 (^[B: $i] : refl(((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type))))),
% 1.33/1.09 inference(bind,[status(th)],[])).
% 1.33/1.09 tff(19,plain,
% 1.33/1.09 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 1.33/1.09 inference(quant_intro,[status(thm)],[18])).
% 1.33/1.09 tff(20,plain,
% 1.33/1.09 (^[B: $i] : rewrite(((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type))))),
% 1.33/1.09 inference(bind,[status(th)],[])).
% 1.33/1.09 tff(21,plain,
% 1.33/1.09 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 1.33/1.09 inference(quant_intro,[status(thm)],[20])).
% 1.33/1.09 tff(22,plain,
% 1.33/1.09 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 1.33/1.09 inference(transitivity,[status(thm)],[21, 19])).
% 1.33/1.09 tff(23,plain,
% 1.33/1.09 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 1.33/1.09 inference(rewrite,[status(thm)],[])).
% 1.33/1.09 tff(24,plain,
% 1.33/1.09 (^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((ilf_type(C, set_type) => ilf_type(cross_product(B, C), set_type)) <=> ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))), (![C: $i] : (ilf_type(C, set_type) => ilf_type(cross_product(B, C), set_type)) <=> ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))), ((ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => ilf_type(cross_product(B, C), set_type))) <=> (ilf_type(B, set_type) => ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type))))), rewrite((ilf_type(B, set_type) => ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))), ((ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => ilf_type(cross_product(B, C), set_type))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))))),
% 1.33/1.09 inference(bind,[status(th)],[])).
% 1.33/1.09 tff(25,plain,
% 1.33/1.09 (![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => ilf_type(cross_product(B, C), set_type))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 1.33/1.09 inference(quant_intro,[status(thm)],[24])).
% 1.33/1.09 tff(26,axiom,(![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => ilf_type(cross_product(B, C), set_type)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p4')).
% 1.33/1.09 tff(27,plain,
% 1.33/1.09 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 1.33/1.09 inference(modus_ponens,[status(thm)],[26, 25])).
% 1.33/1.09 tff(28,plain,
% 1.33/1.09 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 1.33/1.09 inference(modus_ponens,[status(thm)],[27, 23])).
% 1.33/1.09 tff(29,plain,(
% 1.33/1.09 ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 1.33/1.09 inference(skolemize,[status(sab)],[28])).
% 1.33/1.09 tff(30,plain,
% 1.33/1.09 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))),
% 1.33/1.09 inference(modus_ponens,[status(thm)],[29, 22])).
% 1.33/1.09 tff(31,plain,
% 1.33/1.09 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))) | ((~ilf_type(C!11, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(C!11, C), set_type)))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))) | (~ilf_type(C!11, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(C!11, C), set_type)))),
% 1.33/1.09 inference(rewrite,[status(thm)],[])).
% 1.33/1.09 tff(32,plain,
% 1.33/1.09 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))) | ((~ilf_type(C!11, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(C!11, C), set_type)))),
% 1.33/1.09 inference(quant_inst,[status(thm)],[])).
% 1.33/1.09 tff(33,plain,
% 1.33/1.09 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(B, C), set_type)))) | (~ilf_type(C!11, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(C!11, C), set_type))),
% 1.33/1.09 inference(modus_ponens,[status(thm)],[32, 31])).
% 1.33/1.09 tff(34,plain,
% 1.33/1.09 (![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(C!11, C), set_type))),
% 1.33/1.09 inference(unit_resolution,[status(thm)],[33, 30, 17])).
% 1.33/1.09 tff(35,plain,
% 1.33/1.09 (~(ilf_type(B!10, relation_type(C!11, D!12)) | (~ilf_type(D!12, set_type)) | (~subset(B!10, cross_product(C!11, D!12))))),
% 1.33/1.09 inference(and_elim,[status(thm)],[16])).
% 1.33/1.09 tff(36,plain,
% 1.33/1.09 (ilf_type(D!12, set_type)),
% 1.33/1.09 inference(or_elim,[status(thm)],[35])).
% 1.33/1.09 tff(37,plain,
% 1.33/1.09 (((~![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(C!11, C), set_type))) | ((~ilf_type(D!12, set_type)) | ilf_type(cross_product(C!11, D!12), set_type))) <=> ((~![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(C!11, C), set_type))) | (~ilf_type(D!12, set_type)) | ilf_type(cross_product(C!11, D!12), set_type))),
% 1.33/1.09 inference(rewrite,[status(thm)],[])).
% 1.33/1.09 tff(38,plain,
% 1.33/1.09 ((~![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(C!11, C), set_type))) | ((~ilf_type(D!12, set_type)) | ilf_type(cross_product(C!11, D!12), set_type))),
% 1.33/1.09 inference(quant_inst,[status(thm)],[])).
% 1.33/1.09 tff(39,plain,
% 1.33/1.09 ((~![C: $i] : ((~ilf_type(C, set_type)) | ilf_type(cross_product(C!11, C), set_type))) | (~ilf_type(D!12, set_type)) | ilf_type(cross_product(C!11, D!12), set_type)),
% 1.33/1.09 inference(modus_ponens,[status(thm)],[38, 37])).
% 1.33/1.09 tff(40,plain,
% 1.33/1.09 (ilf_type(cross_product(C!11, D!12), set_type)),
% 1.33/1.09 inference(unit_resolution,[status(thm)],[39, 36, 34])).
% 1.33/1.09 tff(41,plain,
% 1.33/1.09 (ilf_type(B!10, set_type)),
% 1.33/1.09 inference(and_elim,[status(thm)],[16])).
% 1.33/1.09 tff(42,plain,
% 1.33/1.09 (^[B: $i] : refl(((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))))))),
% 1.33/1.09 inference(bind,[status(th)],[])).
% 1.33/1.09 tff(43,plain,
% 1.33/1.09 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))),
% 1.33/1.09 inference(quant_intro,[status(thm)],[42])).
% 1.33/1.09 tff(44,plain,
% 1.33/1.09 (^[B: $i] : rewrite(((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))))))),
% 1.33/1.09 inference(bind,[status(th)],[])).
% 1.33/1.09 tff(45,plain,
% 1.33/1.09 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))),
% 1.33/1.09 inference(quant_intro,[status(thm)],[44])).
% 1.33/1.09 tff(46,plain,
% 1.33/1.09 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))),
% 1.33/1.09 inference(transitivity,[status(thm)],[45, 43])).
% 1.33/1.09 tff(47,plain,
% 1.33/1.09 (^[B: $i] : rewrite(((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B)))) & (member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))))))),
% 1.33/1.09 inference(bind,[status(th)],[])).
% 1.33/1.09 tff(48,plain,
% 1.33/1.09 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B)))) & (member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))),
% 1.33/1.09 inference(quant_intro,[status(thm)],[47])).
% 1.33/1.09 tff(49,plain,
% 1.33/1.09 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (member(B, power_set(C)) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B)))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (member(B, power_set(C)) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))))),
% 1.33/1.09 inference(rewrite,[status(thm)],[])).
% 1.33/1.09 tff(50,plain,
% 1.33/1.09 (^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((member(B, power_set(C)) <=> ![D: $i] : (ilf_type(D, set_type) => (member(D, B) => member(D, C)))) <=> (member(B, power_set(C)) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))), ((ilf_type(C, set_type) => (member(B, power_set(C)) <=> ![D: $i] : (ilf_type(D, set_type) => (member(D, B) => member(D, C))))) <=> (ilf_type(C, set_type) => (member(B, power_set(C)) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))))), rewrite((ilf_type(C, set_type) => (member(B, power_set(C)) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) <=> ((~ilf_type(C, set_type)) | (member(B, power_set(C)) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B)))))), ((ilf_type(C, set_type) => (member(B, power_set(C)) <=> ![D: $i] : (ilf_type(D, set_type) => (member(D, B) => member(D, C))))) <=> ((~ilf_type(C, set_type)) | (member(B, power_set(C)) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B)))))))), (![C: $i] : (ilf_type(C, set_type) => (member(B, power_set(C)) <=> ![D: $i] : (ilf_type(D, set_type) => (member(D, B) => member(D, C))))) <=> ![C: $i] : ((~ilf_type(C, set_type)) | (member(B, power_set(C)) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))))), ((ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (member(B, power_set(C)) <=> ![D: $i] : (ilf_type(D, set_type) => (member(D, B) => member(D, C)))))) <=> (ilf_type(B, set_type) => ![C: $i] : ((~ilf_type(C, set_type)) | (member(B, power_set(C)) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B)))))))), rewrite((ilf_type(B, set_type) => ![C: $i] : ((~ilf_type(C, set_type)) | (member(B, power_set(C)) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B)))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (member(B, power_set(C)) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))))), ((ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (member(B, power_set(C)) <=> ![D: $i] : (ilf_type(D, set_type) => (member(D, B) => member(D, C)))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (member(B, power_set(C)) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))))))),
% 1.33/1.09 inference(bind,[status(th)],[])).
% 1.33/1.09 tff(51,plain,
% 1.33/1.09 (![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (member(B, power_set(C)) <=> ![D: $i] : (ilf_type(D, set_type) => (member(D, B) => member(D, C)))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (member(B, power_set(C)) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))))),
% 1.33/1.09 inference(quant_intro,[status(thm)],[50])).
% 1.33/1.09 tff(52,axiom,(![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (member(B, power_set(C)) <=> ![D: $i] : (ilf_type(D, set_type) => (member(D, B) => member(D, C))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p10')).
% 1.33/1.09 tff(53,plain,
% 1.33/1.09 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (member(B, power_set(C)) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))))),
% 1.33/1.09 inference(modus_ponens,[status(thm)],[52, 51])).
% 1.33/1.09 tff(54,plain,
% 1.33/1.09 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (member(B, power_set(C)) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))))),
% 1.33/1.09 inference(modus_ponens,[status(thm)],[53, 49])).
% 1.33/1.09 tff(55,plain,(
% 1.33/1.09 ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B)))) & (member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))),
% 1.33/1.09 inference(skolemize,[status(sab)],[54])).
% 1.33/1.09 tff(56,plain,
% 1.33/1.09 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))),
% 1.33/1.09 inference(modus_ponens,[status(thm)],[55, 48])).
% 1.33/1.09 tff(57,plain,
% 1.33/1.09 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))),
% 1.33/1.09 inference(modus_ponens,[status(thm)],[56, 46])).
% 1.33/1.09 tff(58,plain,
% 1.33/1.09 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))) | ((~ilf_type(B!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B!10, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(C)) | (~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10))))))))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))) | (~ilf_type(B!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B!10, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(C)) | (~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10))))))))))),
% 1.33/1.09 inference(rewrite,[status(thm)],[])).
% 1.33/1.09 tff(59,plain,
% 1.33/1.09 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))) | ((~ilf_type(B!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B!10, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(C)) | (~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10))))))))))),
% 1.33/1.09 inference(quant_inst,[status(thm)],[])).
% 1.33/1.09 tff(60,plain,
% 1.33/1.09 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(member(B, power_set(C)) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))) | (~ilf_type(B!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B!10, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(C)) | (~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10)))))))))),
% 1.33/1.09 inference(modus_ponens,[status(thm)],[59, 58])).
% 1.33/1.09 tff(61,plain,
% 1.33/1.09 (![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B!10, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(C)) | (~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10)))))))))),
% 1.33/1.09 inference(unit_resolution,[status(thm)],[60, 57, 41])).
% 1.33/1.09 tff(62,plain,
% 1.33/1.09 (((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B!10, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(C)) | (~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10)))))))))) | ((~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~member(B!10, power_set(cross_product(C!11, D!12)))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | member(B!10, power_set(cross_product(C!11, D!12))))))))) <=> ((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B!10, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(C)) | (~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10)))))))))) | (~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~member(B!10, power_set(cross_product(C!11, D!12)))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | member(B!10, power_set(cross_product(C!11, D!12))))))))),
% 1.33/1.09 inference(rewrite,[status(thm)],[])).
% 1.33/1.09 tff(63,plain,
% 1.33/1.09 (((~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~member(B!10, power_set(cross_product(C!11, D!12)))) | ![D: $i] : (member(D, cross_product(C!11, D!12)) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(cross_product(C!11, D!12))) | (~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10))))))))) <=> ((~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~member(B!10, power_set(cross_product(C!11, D!12)))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | member(B!10, power_set(cross_product(C!11, D!12))))))))),
% 1.33/1.09 inference(rewrite,[status(thm)],[])).
% 1.33/1.09 tff(64,plain,
% 1.33/1.09 (((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B!10, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(C)) | (~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10)))))))))) | ((~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~member(B!10, power_set(cross_product(C!11, D!12)))) | ![D: $i] : (member(D, cross_product(C!11, D!12)) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(cross_product(C!11, D!12))) | (~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))))))))) <=> ((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B!10, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(C)) | (~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10)))))))))) | ((~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~member(B!10, power_set(cross_product(C!11, D!12)))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | member(B!10, power_set(cross_product(C!11, D!12)))))))))),
% 1.33/1.09 inference(monotonicity,[status(thm)],[63])).
% 1.33/1.09 tff(65,plain,
% 1.33/1.09 (((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B!10, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(C)) | (~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10)))))))))) | ((~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~member(B!10, power_set(cross_product(C!11, D!12)))) | ![D: $i] : (member(D, cross_product(C!11, D!12)) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(cross_product(C!11, D!12))) | (~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))))))))) <=> ((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B!10, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(C)) | (~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10)))))))))) | (~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~member(B!10, power_set(cross_product(C!11, D!12)))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | member(B!10, power_set(cross_product(C!11, D!12))))))))),
% 1.33/1.10 inference(transitivity,[status(thm)],[64, 62])).
% 1.33/1.10 tff(66,plain,
% 1.33/1.10 ((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B!10, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(C)) | (~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10)))))))))) | ((~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~member(B!10, power_set(cross_product(C!11, D!12)))) | ![D: $i] : (member(D, cross_product(C!11, D!12)) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(cross_product(C!11, D!12))) | (~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))))))))),
% 1.33/1.10 inference(quant_inst,[status(thm)],[])).
% 1.33/1.10 tff(67,plain,
% 1.33/1.10 ((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~member(B!10, power_set(C))) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(member(B!10, power_set(C)) | (~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10)))))))))) | (~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~member(B!10, power_set(cross_product(C!11, D!12)))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | member(B!10, power_set(cross_product(C!11, D!12)))))))),
% 1.33/1.10 inference(modus_ponens,[status(thm)],[66, 65])).
% 1.33/1.10 tff(68,plain,
% 1.33/1.10 (~((~((~member(B!10, power_set(cross_product(C!11, D!12)))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | member(B!10, power_set(cross_product(C!11, D!12))))))),
% 1.33/1.10 inference(unit_resolution,[status(thm)],[67, 61, 40])).
% 1.33/1.10 tff(69,plain,
% 1.33/1.10 (((~((~member(B!10, power_set(cross_product(C!11, D!12)))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | member(B!10, power_set(cross_product(C!11, D!12)))))) | ((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | member(B!10, power_set(cross_product(C!11, D!12))))),
% 1.33/1.10 inference(tautology,[status(thm)],[])).
% 1.33/1.10 tff(70,plain,
% 1.33/1.10 ((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | member(B!10, power_set(cross_product(C!11, D!12)))),
% 1.33/1.10 inference(unit_resolution,[status(thm)],[69, 68])).
% 1.33/1.10 tff(71,plain,
% 1.33/1.10 (^[B: $i] : refl(((~ilf_type(B, set_type)) | (~(empty(power_set(B)) | (~ilf_type(power_set(B), set_type))))) <=> ((~ilf_type(B, set_type)) | (~(empty(power_set(B)) | (~ilf_type(power_set(B), set_type))))))),
% 1.33/1.10 inference(bind,[status(th)],[])).
% 1.33/1.10 tff(72,plain,
% 1.33/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | (~(empty(power_set(B)) | (~ilf_type(power_set(B), set_type))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | (~(empty(power_set(B)) | (~ilf_type(power_set(B), set_type)))))),
% 1.33/1.10 inference(quant_intro,[status(thm)],[71])).
% 1.33/1.10 tff(73,plain,
% 1.33/1.10 (^[B: $i] : rewrite(((~ilf_type(B, set_type)) | ((~empty(power_set(B))) & ilf_type(power_set(B), set_type))) <=> ((~ilf_type(B, set_type)) | (~(empty(power_set(B)) | (~ilf_type(power_set(B), set_type))))))),
% 1.33/1.10 inference(bind,[status(th)],[])).
% 1.33/1.10 tff(74,plain,
% 1.33/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ((~empty(power_set(B))) & ilf_type(power_set(B), set_type))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | (~(empty(power_set(B)) | (~ilf_type(power_set(B), set_type)))))),
% 1.33/1.10 inference(quant_intro,[status(thm)],[73])).
% 1.33/1.10 tff(75,plain,
% 1.33/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ((~empty(power_set(B))) & ilf_type(power_set(B), set_type))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ((~empty(power_set(B))) & ilf_type(power_set(B), set_type)))),
% 1.33/1.10 inference(rewrite,[status(thm)],[])).
% 1.33/1.10 tff(76,plain,
% 1.33/1.10 (^[B: $i] : rewrite((ilf_type(B, set_type) => ((~empty(power_set(B))) & ilf_type(power_set(B), set_type))) <=> ((~ilf_type(B, set_type)) | ((~empty(power_set(B))) & ilf_type(power_set(B), set_type))))),
% 1.33/1.10 inference(bind,[status(th)],[])).
% 1.33/1.10 tff(77,plain,
% 1.33/1.10 (![B: $i] : (ilf_type(B, set_type) => ((~empty(power_set(B))) & ilf_type(power_set(B), set_type))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ((~empty(power_set(B))) & ilf_type(power_set(B), set_type)))),
% 1.33/1.10 inference(quant_intro,[status(thm)],[76])).
% 1.33/1.10 tff(78,axiom,(![B: $i] : (ilf_type(B, set_type) => ((~empty(power_set(B))) & ilf_type(power_set(B), set_type)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p11')).
% 1.33/1.10 tff(79,plain,
% 1.33/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ((~empty(power_set(B))) & ilf_type(power_set(B), set_type)))),
% 1.33/1.10 inference(modus_ponens,[status(thm)],[78, 77])).
% 1.33/1.10 tff(80,plain,
% 1.33/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ((~empty(power_set(B))) & ilf_type(power_set(B), set_type)))),
% 1.33/1.10 inference(modus_ponens,[status(thm)],[79, 75])).
% 1.33/1.10 tff(81,plain,(
% 1.33/1.10 ![B: $i] : ((~ilf_type(B, set_type)) | ((~empty(power_set(B))) & ilf_type(power_set(B), set_type)))),
% 1.33/1.10 inference(skolemize,[status(sab)],[80])).
% 1.33/1.10 tff(82,plain,
% 1.33/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | (~(empty(power_set(B)) | (~ilf_type(power_set(B), set_type)))))),
% 1.33/1.10 inference(modus_ponens,[status(thm)],[81, 74])).
% 1.33/1.10 tff(83,plain,
% 1.33/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | (~(empty(power_set(B)) | (~ilf_type(power_set(B), set_type)))))),
% 1.33/1.10 inference(modus_ponens,[status(thm)],[82, 72])).
% 1.33/1.10 tff(84,plain,
% 1.33/1.10 (((~![B: $i] : ((~ilf_type(B, set_type)) | (~(empty(power_set(B)) | (~ilf_type(power_set(B), set_type)))))) | ((~ilf_type(cross_product(C!11, D!12), set_type)) | (~(empty(power_set(cross_product(C!11, D!12))) | (~ilf_type(power_set(cross_product(C!11, D!12)), set_type)))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | (~(empty(power_set(B)) | (~ilf_type(power_set(B), set_type)))))) | (~ilf_type(cross_product(C!11, D!12), set_type)) | (~(empty(power_set(cross_product(C!11, D!12))) | (~ilf_type(power_set(cross_product(C!11, D!12)), set_type)))))),
% 1.33/1.10 inference(rewrite,[status(thm)],[])).
% 1.33/1.10 tff(85,plain,
% 1.33/1.10 ((~![B: $i] : ((~ilf_type(B, set_type)) | (~(empty(power_set(B)) | (~ilf_type(power_set(B), set_type)))))) | ((~ilf_type(cross_product(C!11, D!12), set_type)) | (~(empty(power_set(cross_product(C!11, D!12))) | (~ilf_type(power_set(cross_product(C!11, D!12)), set_type)))))),
% 1.33/1.10 inference(quant_inst,[status(thm)],[])).
% 1.33/1.10 tff(86,plain,
% 1.33/1.10 ((~![B: $i] : ((~ilf_type(B, set_type)) | (~(empty(power_set(B)) | (~ilf_type(power_set(B), set_type)))))) | (~ilf_type(cross_product(C!11, D!12), set_type)) | (~(empty(power_set(cross_product(C!11, D!12))) | (~ilf_type(power_set(cross_product(C!11, D!12)), set_type))))),
% 1.33/1.10 inference(modus_ponens,[status(thm)],[85, 84])).
% 1.33/1.10 tff(87,plain,
% 1.33/1.10 (~(empty(power_set(cross_product(C!11, D!12))) | (~ilf_type(power_set(cross_product(C!11, D!12)), set_type)))),
% 1.33/1.10 inference(unit_resolution,[status(thm)],[86, 83, 40])).
% 1.33/1.10 tff(88,plain,
% 1.33/1.10 ((empty(power_set(cross_product(C!11, D!12))) | (~ilf_type(power_set(cross_product(C!11, D!12)), set_type))) | (~empty(power_set(cross_product(C!11, D!12))))),
% 1.33/1.10 inference(tautology,[status(thm)],[])).
% 1.33/1.10 tff(89,plain,
% 1.33/1.10 (~empty(power_set(cross_product(C!11, D!12)))),
% 1.33/1.10 inference(unit_resolution,[status(thm)],[88, 87])).
% 1.33/1.10 tff(90,plain,
% 1.33/1.10 ((empty(power_set(cross_product(C!11, D!12))) | (~ilf_type(power_set(cross_product(C!11, D!12)), set_type))) | ilf_type(power_set(cross_product(C!11, D!12)), set_type)),
% 1.33/1.10 inference(tautology,[status(thm)],[])).
% 1.33/1.10 tff(91,plain,
% 1.33/1.10 (ilf_type(power_set(cross_product(C!11, D!12)), set_type)),
% 1.33/1.10 inference(unit_resolution,[status(thm)],[90, 87])).
% 1.33/1.10 tff(92,plain,
% 1.33/1.10 (^[B: $i] : refl(((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type)))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type)))))),
% 1.33/1.10 inference(bind,[status(th)],[])).
% 1.33/1.10 tff(93,plain,
% 1.33/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type)))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type))))),
% 1.33/1.10 inference(quant_intro,[status(thm)],[92])).
% 1.33/1.10 tff(94,plain,
% 1.33/1.10 (^[B: $i] : rewrite(((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type)))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type)))))),
% 1.33/1.10 inference(bind,[status(th)],[])).
% 1.33/1.10 tff(95,plain,
% 1.33/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type)))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type))))),
% 1.33/1.10 inference(quant_intro,[status(thm)],[94])).
% 1.33/1.10 tff(96,plain,
% 1.33/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type)))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type))))),
% 1.33/1.10 inference(transitivity,[status(thm)],[95, 93])).
% 1.33/1.10 tff(97,plain,
% 1.33/1.10 (^[B: $i] : rewrite(((~ilf_type(B, set_type)) | ![C: $i] : ((~((~empty(C)) & ilf_type(C, set_type))) | (ilf_type(B, member_type(C)) <=> member(B, C)))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type)))))),
% 1.33/1.10 inference(bind,[status(th)],[])).
% 1.33/1.10 tff(98,plain,
% 1.33/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~((~empty(C)) & ilf_type(C, set_type))) | (ilf_type(B, member_type(C)) <=> member(B, C)))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type))))),
% 1.33/1.10 inference(quant_intro,[status(thm)],[97])).
% 1.33/1.10 tff(99,plain,
% 1.33/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~((~empty(C)) & ilf_type(C, set_type))) | (ilf_type(B, member_type(C)) <=> member(B, C)))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~((~empty(C)) & ilf_type(C, set_type))) | (ilf_type(B, member_type(C)) <=> member(B, C))))),
% 1.33/1.10 inference(rewrite,[status(thm)],[])).
% 1.33/1.10 tff(100,plain,
% 1.33/1.10 (^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((((~empty(C)) & ilf_type(C, set_type)) => (ilf_type(B, member_type(C)) <=> member(B, C))) <=> ((~((~empty(C)) & ilf_type(C, set_type))) | (ilf_type(B, member_type(C)) <=> member(B, C))))), (![C: $i] : (((~empty(C)) & ilf_type(C, set_type)) => (ilf_type(B, member_type(C)) <=> member(B, C))) <=> ![C: $i] : ((~((~empty(C)) & ilf_type(C, set_type))) | (ilf_type(B, member_type(C)) <=> member(B, C))))), ((ilf_type(B, set_type) => ![C: $i] : (((~empty(C)) & ilf_type(C, set_type)) => (ilf_type(B, member_type(C)) <=> member(B, C)))) <=> (ilf_type(B, set_type) => ![C: $i] : ((~((~empty(C)) & ilf_type(C, set_type))) | (ilf_type(B, member_type(C)) <=> member(B, C)))))), rewrite((ilf_type(B, set_type) => ![C: $i] : ((~((~empty(C)) & ilf_type(C, set_type))) | (ilf_type(B, member_type(C)) <=> member(B, C)))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~((~empty(C)) & ilf_type(C, set_type))) | (ilf_type(B, member_type(C)) <=> member(B, C))))), ((ilf_type(B, set_type) => ![C: $i] : (((~empty(C)) & ilf_type(C, set_type)) => (ilf_type(B, member_type(C)) <=> member(B, C)))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~((~empty(C)) & ilf_type(C, set_type))) | (ilf_type(B, member_type(C)) <=> member(B, C))))))),
% 1.33/1.10 inference(bind,[status(th)],[])).
% 1.33/1.10 tff(101,plain,
% 1.33/1.10 (![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (((~empty(C)) & ilf_type(C, set_type)) => (ilf_type(B, member_type(C)) <=> member(B, C)))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~((~empty(C)) & ilf_type(C, set_type))) | (ilf_type(B, member_type(C)) <=> member(B, C))))),
% 1.33/1.10 inference(quant_intro,[status(thm)],[100])).
% 1.33/1.10 tff(102,axiom,(![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (((~empty(C)) & ilf_type(C, set_type)) => (ilf_type(B, member_type(C)) <=> member(B, C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p12')).
% 1.33/1.10 tff(103,plain,
% 1.33/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~((~empty(C)) & ilf_type(C, set_type))) | (ilf_type(B, member_type(C)) <=> member(B, C))))),
% 1.33/1.10 inference(modus_ponens,[status(thm)],[102, 101])).
% 1.33/1.10 tff(104,plain,
% 1.33/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~((~empty(C)) & ilf_type(C, set_type))) | (ilf_type(B, member_type(C)) <=> member(B, C))))),
% 1.33/1.10 inference(modus_ponens,[status(thm)],[103, 99])).
% 1.33/1.10 tff(105,plain,(
% 1.33/1.10 ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~((~empty(C)) & ilf_type(C, set_type))) | (ilf_type(B, member_type(C)) <=> member(B, C))))),
% 1.33/1.10 inference(skolemize,[status(sab)],[104])).
% 1.33/1.10 tff(106,plain,
% 1.33/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type))))),
% 1.33/1.10 inference(modus_ponens,[status(thm)],[105, 98])).
% 1.33/1.10 tff(107,plain,
% 1.33/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type))))),
% 1.33/1.10 inference(modus_ponens,[status(thm)],[106, 96])).
% 1.33/1.10 tff(108,plain,
% 1.33/1.10 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type))))) | ((~ilf_type(B!10, set_type)) | ![C: $i] : (empty(C) | (~ilf_type(C, set_type)) | (ilf_type(B!10, member_type(C)) <=> member(B!10, C))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type))))) | (~ilf_type(B!10, set_type)) | ![C: $i] : (empty(C) | (~ilf_type(C, set_type)) | (ilf_type(B!10, member_type(C)) <=> member(B!10, C))))),
% 1.33/1.10 inference(rewrite,[status(thm)],[])).
% 1.33/1.10 tff(109,plain,
% 1.33/1.10 (((~ilf_type(B!10, set_type)) | ![C: $i] : ((ilf_type(B!10, member_type(C)) <=> member(B!10, C)) | empty(C) | (~ilf_type(C, set_type)))) <=> ((~ilf_type(B!10, set_type)) | ![C: $i] : (empty(C) | (~ilf_type(C, set_type)) | (ilf_type(B!10, member_type(C)) <=> member(B!10, C))))),
% 1.33/1.10 inference(rewrite,[status(thm)],[])).
% 1.33/1.10 tff(110,plain,
% 1.33/1.10 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type))))) | ((~ilf_type(B!10, set_type)) | ![C: $i] : ((ilf_type(B!10, member_type(C)) <=> member(B!10, C)) | empty(C) | (~ilf_type(C, set_type))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type))))) | ((~ilf_type(B!10, set_type)) | ![C: $i] : (empty(C) | (~ilf_type(C, set_type)) | (ilf_type(B!10, member_type(C)) <=> member(B!10, C)))))),
% 1.33/1.10 inference(monotonicity,[status(thm)],[109])).
% 1.33/1.10 tff(111,plain,
% 1.33/1.10 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type))))) | ((~ilf_type(B!10, set_type)) | ![C: $i] : ((ilf_type(B!10, member_type(C)) <=> member(B!10, C)) | empty(C) | (~ilf_type(C, set_type))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type))))) | (~ilf_type(B!10, set_type)) | ![C: $i] : (empty(C) | (~ilf_type(C, set_type)) | (ilf_type(B!10, member_type(C)) <=> member(B!10, C))))),
% 1.33/1.10 inference(transitivity,[status(thm)],[110, 108])).
% 1.33/1.10 tff(112,plain,
% 1.33/1.10 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type))))) | ((~ilf_type(B!10, set_type)) | ![C: $i] : ((ilf_type(B!10, member_type(C)) <=> member(B!10, C)) | empty(C) | (~ilf_type(C, set_type))))),
% 1.33/1.10 inference(quant_inst,[status(thm)],[])).
% 1.33/1.10 tff(113,plain,
% 1.33/1.10 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((ilf_type(B, member_type(C)) <=> member(B, C)) | empty(C) | (~ilf_type(C, set_type))))) | (~ilf_type(B!10, set_type)) | ![C: $i] : (empty(C) | (~ilf_type(C, set_type)) | (ilf_type(B!10, member_type(C)) <=> member(B!10, C)))),
% 1.33/1.10 inference(modus_ponens,[status(thm)],[112, 111])).
% 1.33/1.10 tff(114,plain,
% 1.33/1.10 (![C: $i] : (empty(C) | (~ilf_type(C, set_type)) | (ilf_type(B!10, member_type(C)) <=> member(B!10, C)))),
% 1.33/1.10 inference(unit_resolution,[status(thm)],[113, 107, 41])).
% 1.33/1.10 tff(115,plain,
% 1.33/1.10 (((~![C: $i] : (empty(C) | (~ilf_type(C, set_type)) | (ilf_type(B!10, member_type(C)) <=> member(B!10, C)))) | (empty(power_set(cross_product(C!11, D!12))) | (~ilf_type(power_set(cross_product(C!11, D!12)), set_type)) | (ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12)))) <=> member(B!10, power_set(cross_product(C!11, D!12)))))) <=> ((~![C: $i] : (empty(C) | (~ilf_type(C, set_type)) | (ilf_type(B!10, member_type(C)) <=> member(B!10, C)))) | empty(power_set(cross_product(C!11, D!12))) | (~ilf_type(power_set(cross_product(C!11, D!12)), set_type)) | (ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12)))) <=> member(B!10, power_set(cross_product(C!11, D!12)))))),
% 1.33/1.10 inference(rewrite,[status(thm)],[])).
% 1.33/1.10 tff(116,plain,
% 1.33/1.10 ((~![C: $i] : (empty(C) | (~ilf_type(C, set_type)) | (ilf_type(B!10, member_type(C)) <=> member(B!10, C)))) | (empty(power_set(cross_product(C!11, D!12))) | (~ilf_type(power_set(cross_product(C!11, D!12)), set_type)) | (ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12)))) <=> member(B!10, power_set(cross_product(C!11, D!12)))))),
% 1.33/1.10 inference(quant_inst,[status(thm)],[])).
% 1.33/1.10 tff(117,plain,
% 1.33/1.10 ((~![C: $i] : (empty(C) | (~ilf_type(C, set_type)) | (ilf_type(B!10, member_type(C)) <=> member(B!10, C)))) | empty(power_set(cross_product(C!11, D!12))) | (~ilf_type(power_set(cross_product(C!11, D!12)), set_type)) | (ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12)))) <=> member(B!10, power_set(cross_product(C!11, D!12))))),
% 1.33/1.10 inference(modus_ponens,[status(thm)],[116, 115])).
% 1.33/1.10 tff(118,plain,
% 1.33/1.10 (empty(power_set(cross_product(C!11, D!12))) | (~ilf_type(power_set(cross_product(C!11, D!12)), set_type)) | (ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12)))) <=> member(B!10, power_set(cross_product(C!11, D!12))))),
% 1.33/1.10 inference(unit_resolution,[status(thm)],[117, 114])).
% 1.33/1.10 tff(119,plain,
% 1.33/1.10 (ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12)))) <=> member(B!10, power_set(cross_product(C!11, D!12)))),
% 1.33/1.10 inference(unit_resolution,[status(thm)],[118, 91, 89])).
% 1.33/1.10 tff(120,plain,
% 1.33/1.10 (^[B: $i] : refl(((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B)))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B)))))))),
% 1.33/1.10 inference(bind,[status(th)],[])).
% 1.33/1.10 tff(121,plain,
% 1.33/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B)))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))),
% 1.33/1.10 inference(quant_intro,[status(thm)],[120])).
% 1.33/1.10 tff(122,plain,
% 1.33/1.10 (^[B: $i] : rewrite(((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B)))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B)))))))),
% 1.33/1.10 inference(bind,[status(th)],[])).
% 1.33/1.10 tff(123,plain,
% 1.33/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B)))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))),
% 1.33/1.10 inference(quant_intro,[status(thm)],[122])).
% 1.33/1.10 tff(124,plain,
% 1.33/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B)))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))),
% 1.33/1.10 inference(transitivity,[status(thm)],[123, 121])).
% 1.33/1.10 tff(125,plain,
% 1.33/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B)))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))),
% 1.33/1.10 inference(rewrite,[status(thm)],[])).
% 1.33/1.10 tff(126,plain,
% 1.33/1.10 (^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((ilf_type(C, set_type) => (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))) <=> ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))), (![C: $i] : (ilf_type(C, set_type) => (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))) <=> ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))), ((ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B)))))) <=> (ilf_type(B, set_type) => ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B)))))))), rewrite((ilf_type(B, set_type) => ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B)))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))), ((ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B)))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))))),
% 1.33/1.10 inference(bind,[status(th)],[])).
% 1.33/1.10 tff(127,plain,
% 1.33/1.10 (![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B)))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))),
% 1.33/1.10 inference(quant_intro,[status(thm)],[126])).
% 1.33/1.10 tff(128,axiom,(![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p7')).
% 1.33/1.10 tff(129,plain,
% 1.33/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))),
% 1.33/1.10 inference(modus_ponens,[status(thm)],[128, 127])).
% 1.33/1.10 tff(130,plain,
% 1.33/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))),
% 1.33/1.10 inference(modus_ponens,[status(thm)],[129, 125])).
% 1.33/1.10 tff(131,plain,(
% 1.33/1.10 ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))),
% 1.33/1.10 inference(skolemize,[status(sab)],[130])).
% 1.33/1.10 tff(132,plain,
% 1.33/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))),
% 1.33/1.10 inference(modus_ponens,[status(thm)],[131, 124])).
% 1.33/1.10 tff(133,plain,
% 1.33/1.10 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))) | ((~ilf_type(cross_product(C!11, D!12), set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(cross_product(C!11, D!12))) <=> ilf_type(C, member_type(power_set(cross_product(C!11, D!12)))))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))) | (~ilf_type(cross_product(C!11, D!12), set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(cross_product(C!11, D!12))) <=> ilf_type(C, member_type(power_set(cross_product(C!11, D!12)))))))),
% 1.33/1.10 inference(rewrite,[status(thm)],[])).
% 1.33/1.10 tff(134,plain,
% 1.33/1.10 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))) | ((~ilf_type(cross_product(C!11, D!12), set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(cross_product(C!11, D!12))) <=> ilf_type(C, member_type(power_set(cross_product(C!11, D!12)))))))),
% 1.33/1.10 inference(quant_inst,[status(thm)],[])).
% 1.33/1.10 tff(135,plain,
% 1.33/1.10 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(B)) <=> ilf_type(C, member_type(power_set(B))))))) | (~ilf_type(cross_product(C!11, D!12), set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(cross_product(C!11, D!12))) <=> ilf_type(C, member_type(power_set(cross_product(C!11, D!12))))))),
% 1.33/1.10 inference(modus_ponens,[status(thm)],[134, 133])).
% 1.33/1.10 tff(136,plain,
% 1.33/1.10 (![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(cross_product(C!11, D!12))) <=> ilf_type(C, member_type(power_set(cross_product(C!11, D!12))))))),
% 1.33/1.10 inference(unit_resolution,[status(thm)],[135, 132, 40])).
% 1.33/1.10 tff(137,plain,
% 1.33/1.10 (((~![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(cross_product(C!11, D!12))) <=> ilf_type(C, member_type(power_set(cross_product(C!11, D!12))))))) | ((~ilf_type(B!10, set_type)) | (ilf_type(B!10, subset_type(cross_product(C!11, D!12))) <=> ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12))))))) <=> ((~![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(cross_product(C!11, D!12))) <=> ilf_type(C, member_type(power_set(cross_product(C!11, D!12))))))) | (~ilf_type(B!10, set_type)) | (ilf_type(B!10, subset_type(cross_product(C!11, D!12))) <=> ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12))))))),
% 1.33/1.10 inference(rewrite,[status(thm)],[])).
% 1.33/1.10 tff(138,plain,
% 1.33/1.10 ((~![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(cross_product(C!11, D!12))) <=> ilf_type(C, member_type(power_set(cross_product(C!11, D!12))))))) | ((~ilf_type(B!10, set_type)) | (ilf_type(B!10, subset_type(cross_product(C!11, D!12))) <=> ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12))))))),
% 1.33/1.10 inference(quant_inst,[status(thm)],[])).
% 1.33/1.10 tff(139,plain,
% 1.33/1.10 ((~![C: $i] : ((~ilf_type(C, set_type)) | (ilf_type(C, subset_type(cross_product(C!11, D!12))) <=> ilf_type(C, member_type(power_set(cross_product(C!11, D!12))))))) | (~ilf_type(B!10, set_type)) | (ilf_type(B!10, subset_type(cross_product(C!11, D!12))) <=> ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12)))))),
% 1.33/1.10 inference(modus_ponens,[status(thm)],[138, 137])).
% 1.33/1.10 tff(140,plain,
% 1.33/1.10 (ilf_type(B!10, subset_type(cross_product(C!11, D!12))) <=> ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12))))),
% 1.33/1.10 inference(unit_resolution,[status(thm)],[139, 41, 136])).
% 1.33/1.10 tff(141,plain,
% 1.33/1.10 (^[B: $i] : refl(((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C))))))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C))))))))))),
% 1.33/1.10 inference(bind,[status(th)],[])).
% 1.33/1.10 tff(142,plain,
% 1.33/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C))))))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))))),
% 1.33/1.10 inference(quant_intro,[status(thm)],[141])).
% 1.33/1.10 tff(143,plain,
% 1.33/1.10 (^[B: $i] : rewrite(((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C))))))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C))))))))))),
% 1.33/1.10 inference(bind,[status(th)],[])).
% 1.33/1.10 tff(144,plain,
% 1.33/1.10 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C))))))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))))),
% 1.33/1.11 inference(quant_intro,[status(thm)],[143])).
% 1.33/1.11 tff(145,plain,
% 1.33/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C))))))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))))),
% 1.33/1.11 inference(transitivity,[status(thm)],[144, 142])).
% 1.33/1.11 tff(146,plain,
% 1.33/1.11 (^[B: $i] : rewrite(((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C))))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C))))))))))),
% 1.33/1.11 inference(bind,[status(th)],[])).
% 1.33/1.11 tff(147,plain,
% 1.33/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C))))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))))),
% 1.33/1.11 inference(quant_intro,[status(thm)],[146])).
% 1.33/1.11 tff(148,plain,
% 1.33/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C))))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))),
% 1.33/1.11 inference(rewrite,[status(thm)],[])).
% 1.33/1.11 tff(149,plain,
% 1.33/1.11 (^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((![D: $i] : (ilf_type(D, subset_type(cross_product(B, C))) => ilf_type(D, relation_type(B, C))) & ![E: $i] : (ilf_type(E, relation_type(B, C)) => ilf_type(E, subset_type(cross_product(B, C))))) <=> (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))), ((ilf_type(C, set_type) => (![D: $i] : (ilf_type(D, subset_type(cross_product(B, C))) => ilf_type(D, relation_type(B, C))) & ![E: $i] : (ilf_type(E, relation_type(B, C)) => ilf_type(E, subset_type(cross_product(B, C)))))) <=> (ilf_type(C, set_type) => (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))), rewrite((ilf_type(C, set_type) => (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))) <=> ((~ilf_type(C, set_type)) | (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C))))))), ((ilf_type(C, set_type) => (![D: $i] : (ilf_type(D, subset_type(cross_product(B, C))) => ilf_type(D, relation_type(B, C))) & ![E: $i] : (ilf_type(E, relation_type(B, C)) => ilf_type(E, subset_type(cross_product(B, C)))))) <=> ((~ilf_type(C, set_type)) | (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C))))))))), (![C: $i] : (ilf_type(C, set_type) => (![D: $i] : (ilf_type(D, subset_type(cross_product(B, C))) => ilf_type(D, relation_type(B, C))) & ![E: $i] : (ilf_type(E, relation_type(B, C)) => ilf_type(E, subset_type(cross_product(B, C)))))) <=> ![C: $i] : ((~ilf_type(C, set_type)) | (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))), ((ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (![D: $i] : (ilf_type(D, subset_type(cross_product(B, C))) => ilf_type(D, relation_type(B, C))) & ![E: $i] : (ilf_type(E, relation_type(B, C)) => ilf_type(E, subset_type(cross_product(B, C))))))) <=> (ilf_type(B, set_type) => ![C: $i] : ((~ilf_type(C, set_type)) | (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C))))))))), rewrite((ilf_type(B, set_type) => ![C: $i] : ((~ilf_type(C, set_type)) | (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C))))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))), ((ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (![D: $i] : (ilf_type(D, subset_type(cross_product(B, C))) => ilf_type(D, relation_type(B, C))) & ![E: $i] : (ilf_type(E, relation_type(B, C)) => ilf_type(E, subset_type(cross_product(B, C))))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))))),
% 1.33/1.11 inference(bind,[status(th)],[])).
% 1.33/1.11 tff(150,plain,
% 1.33/1.11 (![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (![D: $i] : (ilf_type(D, subset_type(cross_product(B, C))) => ilf_type(D, relation_type(B, C))) & ![E: $i] : (ilf_type(E, relation_type(B, C)) => ilf_type(E, subset_type(cross_product(B, C))))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))),
% 1.33/1.11 inference(quant_intro,[status(thm)],[149])).
% 1.33/1.11 tff(151,axiom,(![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (![D: $i] : (ilf_type(D, subset_type(cross_product(B, C))) => ilf_type(D, relation_type(B, C))) & ![E: $i] : (ilf_type(E, relation_type(B, C)) => ilf_type(E, subset_type(cross_product(B, C)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p1')).
% 1.33/1.11 tff(152,plain,
% 1.33/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))),
% 1.33/1.11 inference(modus_ponens,[status(thm)],[151, 150])).
% 1.33/1.11 tff(153,plain,
% 1.33/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))),
% 1.33/1.11 inference(modus_ponens,[status(thm)],[152, 148])).
% 1.33/1.11 tff(154,plain,(
% 1.33/1.11 ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C))) & ![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))),
% 1.33/1.11 inference(skolemize,[status(sab)],[153])).
% 1.33/1.11 tff(155,plain,
% 1.33/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))))),
% 1.33/1.11 inference(modus_ponens,[status(thm)],[154, 147])).
% 1.33/1.11 tff(156,plain,
% 1.33/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))))),
% 1.33/1.11 inference(modus_ponens,[status(thm)],[155, 145])).
% 1.33/1.11 tff(157,plain,
% 1.33/1.11 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))))) | ((~ilf_type(C!11, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, C)))) | ilf_type(D, relation_type(C!11, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(C!11, C))) | ilf_type(E, subset_type(cross_product(C!11, C)))))))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))))) | (~ilf_type(C!11, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, C)))) | ilf_type(D, relation_type(C!11, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(C!11, C))) | ilf_type(E, subset_type(cross_product(C!11, C)))))))))),
% 1.33/1.11 inference(rewrite,[status(thm)],[])).
% 1.33/1.11 tff(158,plain,
% 1.33/1.11 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))))) | ((~ilf_type(C!11, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, C)))) | ilf_type(D, relation_type(C!11, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(C!11, C))) | ilf_type(E, subset_type(cross_product(C!11, C)))))))))),
% 1.33/1.11 inference(quant_inst,[status(thm)],[])).
% 1.33/1.11 tff(159,plain,
% 1.33/1.11 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(B, C)))) | ilf_type(D, relation_type(B, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(B, C))) | ilf_type(E, subset_type(cross_product(B, C)))))))))) | (~ilf_type(C!11, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, C)))) | ilf_type(D, relation_type(C!11, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(C!11, C))) | ilf_type(E, subset_type(cross_product(C!11, C))))))))),
% 1.33/1.11 inference(modus_ponens,[status(thm)],[158, 157])).
% 1.33/1.11 tff(160,plain,
% 1.33/1.11 (![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, C)))) | ilf_type(D, relation_type(C!11, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(C!11, C))) | ilf_type(E, subset_type(cross_product(C!11, C))))))))),
% 1.33/1.11 inference(unit_resolution,[status(thm)],[159, 156, 17])).
% 1.33/1.11 tff(161,plain,
% 1.33/1.11 (((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, C)))) | ilf_type(D, relation_type(C!11, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(C!11, C))) | ilf_type(E, subset_type(cross_product(C!11, C))))))))) | ((~ilf_type(D!12, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, D!12)))) | ilf_type(D, relation_type(C!11, D!12)))) | (~![E: $i] : ((~ilf_type(E, relation_type(C!11, D!12))) | ilf_type(E, subset_type(cross_product(C!11, D!12))))))))) <=> ((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, C)))) | ilf_type(D, relation_type(C!11, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(C!11, C))) | ilf_type(E, subset_type(cross_product(C!11, C))))))))) | (~ilf_type(D!12, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, D!12)))) | ilf_type(D, relation_type(C!11, D!12)))) | (~![E: $i] : ((~ilf_type(E, relation_type(C!11, D!12))) | ilf_type(E, subset_type(cross_product(C!11, D!12))))))))),
% 1.33/1.11 inference(rewrite,[status(thm)],[])).
% 1.33/1.11 tff(162,plain,
% 1.33/1.11 ((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, C)))) | ilf_type(D, relation_type(C!11, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(C!11, C))) | ilf_type(E, subset_type(cross_product(C!11, C))))))))) | ((~ilf_type(D!12, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, D!12)))) | ilf_type(D, relation_type(C!11, D!12)))) | (~![E: $i] : ((~ilf_type(E, relation_type(C!11, D!12))) | ilf_type(E, subset_type(cross_product(C!11, D!12))))))))),
% 1.33/1.11 inference(quant_inst,[status(thm)],[])).
% 1.33/1.11 tff(163,plain,
% 1.33/1.11 ((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, C)))) | ilf_type(D, relation_type(C!11, C)))) | (~![E: $i] : ((~ilf_type(E, relation_type(C!11, C))) | ilf_type(E, subset_type(cross_product(C!11, C))))))))) | (~ilf_type(D!12, set_type)) | (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, D!12)))) | ilf_type(D, relation_type(C!11, D!12)))) | (~![E: $i] : ((~ilf_type(E, relation_type(C!11, D!12))) | ilf_type(E, subset_type(cross_product(C!11, D!12)))))))),
% 1.33/1.11 inference(modus_ponens,[status(thm)],[162, 161])).
% 1.33/1.11 tff(164,plain,
% 1.33/1.11 (~((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, D!12)))) | ilf_type(D, relation_type(C!11, D!12)))) | (~![E: $i] : ((~ilf_type(E, relation_type(C!11, D!12))) | ilf_type(E, subset_type(cross_product(C!11, D!12))))))),
% 1.33/1.11 inference(unit_resolution,[status(thm)],[163, 36, 160])).
% 1.33/1.11 tff(165,plain,
% 1.33/1.11 (((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, D!12)))) | ilf_type(D, relation_type(C!11, D!12)))) | (~![E: $i] : ((~ilf_type(E, relation_type(C!11, D!12))) | ilf_type(E, subset_type(cross_product(C!11, D!12)))))) | ![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, D!12)))) | ilf_type(D, relation_type(C!11, D!12)))),
% 1.33/1.11 inference(tautology,[status(thm)],[])).
% 1.33/1.11 tff(166,plain,
% 1.33/1.11 (![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, D!12)))) | ilf_type(D, relation_type(C!11, D!12)))),
% 1.33/1.11 inference(unit_resolution,[status(thm)],[165, 164])).
% 1.33/1.11 tff(167,plain,
% 1.33/1.11 (~ilf_type(B!10, relation_type(C!11, D!12))),
% 1.33/1.11 inference(or_elim,[status(thm)],[35])).
% 1.33/1.11 tff(168,plain,
% 1.33/1.11 (((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, D!12)))) | ilf_type(D, relation_type(C!11, D!12)))) | ((~ilf_type(B!10, subset_type(cross_product(C!11, D!12)))) | ilf_type(B!10, relation_type(C!11, D!12)))) <=> ((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, D!12)))) | ilf_type(D, relation_type(C!11, D!12)))) | (~ilf_type(B!10, subset_type(cross_product(C!11, D!12)))) | ilf_type(B!10, relation_type(C!11, D!12)))),
% 1.33/1.11 inference(rewrite,[status(thm)],[])).
% 1.33/1.11 tff(169,plain,
% 1.33/1.11 ((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, D!12)))) | ilf_type(D, relation_type(C!11, D!12)))) | ((~ilf_type(B!10, subset_type(cross_product(C!11, D!12)))) | ilf_type(B!10, relation_type(C!11, D!12)))),
% 1.33/1.11 inference(quant_inst,[status(thm)],[])).
% 1.33/1.11 tff(170,plain,
% 1.33/1.11 ((~![D: $i] : ((~ilf_type(D, subset_type(cross_product(C!11, D!12)))) | ilf_type(D, relation_type(C!11, D!12)))) | (~ilf_type(B!10, subset_type(cross_product(C!11, D!12)))) | ilf_type(B!10, relation_type(C!11, D!12))),
% 1.33/1.11 inference(modus_ponens,[status(thm)],[169, 168])).
% 1.33/1.11 tff(171,plain,
% 1.33/1.11 (~ilf_type(B!10, subset_type(cross_product(C!11, D!12)))),
% 1.33/1.11 inference(unit_resolution,[status(thm)],[170, 167, 166])).
% 1.33/1.11 tff(172,plain,
% 1.33/1.11 ((~(ilf_type(B!10, subset_type(cross_product(C!11, D!12))) <=> ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12)))))) | ilf_type(B!10, subset_type(cross_product(C!11, D!12))) | (~ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12)))))),
% 1.33/1.11 inference(tautology,[status(thm)],[])).
% 1.33/1.11 tff(173,plain,
% 1.33/1.11 ((~(ilf_type(B!10, subset_type(cross_product(C!11, D!12))) <=> ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12)))))) | (~ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12)))))),
% 1.33/1.11 inference(unit_resolution,[status(thm)],[172, 171])).
% 1.33/1.11 tff(174,plain,
% 1.33/1.11 (~ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12))))),
% 1.33/1.11 inference(unit_resolution,[status(thm)],[173, 140])).
% 1.33/1.11 tff(175,plain,
% 1.33/1.11 ((~(ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12)))) <=> member(B!10, power_set(cross_product(C!11, D!12))))) | ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12)))) | (~member(B!10, power_set(cross_product(C!11, D!12))))),
% 1.33/1.11 inference(tautology,[status(thm)],[])).
% 1.33/1.11 tff(176,plain,
% 1.33/1.11 ((~(ilf_type(B!10, member_type(power_set(cross_product(C!11, D!12)))) <=> member(B!10, power_set(cross_product(C!11, D!12))))) | (~member(B!10, power_set(cross_product(C!11, D!12))))),
% 1.33/1.11 inference(unit_resolution,[status(thm)],[175, 174])).
% 1.33/1.11 tff(177,plain,
% 1.33/1.11 (~member(B!10, power_set(cross_product(C!11, D!12)))),
% 1.33/1.11 inference(unit_resolution,[status(thm)],[176, 119])).
% 1.33/1.11 tff(178,plain,
% 1.33/1.11 ((~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | member(B!10, power_set(cross_product(C!11, D!12))))) | (~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | member(B!10, power_set(cross_product(C!11, D!12)))),
% 1.33/1.11 inference(tautology,[status(thm)],[])).
% 1.33/1.11 tff(179,plain,
% 1.33/1.11 (~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))),
% 1.33/1.11 inference(unit_resolution,[status(thm)],[178, 177, 70])).
% 1.33/1.11 tff(180,plain,
% 1.33/1.11 ((member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10))) | member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)),
% 1.33/1.11 inference(tautology,[status(thm)],[])).
% 1.33/1.11 tff(181,plain,
% 1.33/1.11 (member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)),
% 1.33/1.11 inference(unit_resolution,[status(thm)],[180, 179])).
% 1.33/1.11 tff(182,plain,
% 1.33/1.11 ((member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10))) | ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)),
% 1.33/1.11 inference(tautology,[status(thm)],[])).
% 1.33/1.11 tff(183,plain,
% 1.33/1.11 (ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)),
% 1.33/1.11 inference(unit_resolution,[status(thm)],[182, 179])).
% 1.33/1.11 tff(184,plain,
% 1.33/1.11 ((member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10))) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)))),
% 1.33/1.11 inference(tautology,[status(thm)],[])).
% 1.33/1.11 tff(185,plain,
% 1.33/1.11 (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12))),
% 1.33/1.11 inference(unit_resolution,[status(thm)],[184, 179])).
% 1.33/1.11 tff(186,plain,
% 1.33/1.11 (^[B: $i] : refl(((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))))))),
% 1.33/1.11 inference(bind,[status(th)],[])).
% 1.33/1.11 tff(187,plain,
% 1.33/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))),
% 1.33/1.11 inference(quant_intro,[status(thm)],[186])).
% 1.33/1.11 tff(188,plain,
% 1.33/1.11 (^[B: $i] : rewrite(((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))))))),
% 1.33/1.11 inference(bind,[status(th)],[])).
% 1.33/1.11 tff(189,plain,
% 1.33/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))),
% 1.33/1.11 inference(quant_intro,[status(thm)],[188])).
% 1.33/1.11 tff(190,plain,
% 1.33/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))),
% 1.33/1.11 inference(transitivity,[status(thm)],[189, 187])).
% 1.33/1.11 tff(191,plain,
% 1.33/1.11 (^[B: $i] : rewrite(((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B)))) & (subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))))))),
% 1.33/1.11 inference(bind,[status(th)],[])).
% 1.33/1.11 tff(192,plain,
% 1.33/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B)))) & (subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B)))))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))),
% 1.33/1.11 inference(quant_intro,[status(thm)],[191])).
% 1.33/1.11 tff(193,plain,
% 1.33/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (subset(B, C) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B)))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (subset(B, C) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))))),
% 1.33/1.11 inference(rewrite,[status(thm)],[])).
% 1.33/1.11 tff(194,plain,
% 1.33/1.11 (^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((subset(B, C) <=> ![D: $i] : (ilf_type(D, set_type) => (member(D, B) => member(D, C)))) <=> (subset(B, C) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))), ((ilf_type(C, set_type) => (subset(B, C) <=> ![D: $i] : (ilf_type(D, set_type) => (member(D, B) => member(D, C))))) <=> (ilf_type(C, set_type) => (subset(B, C) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))))), rewrite((ilf_type(C, set_type) => (subset(B, C) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) <=> ((~ilf_type(C, set_type)) | (subset(B, C) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B)))))), ((ilf_type(C, set_type) => (subset(B, C) <=> ![D: $i] : (ilf_type(D, set_type) => (member(D, B) => member(D, C))))) <=> ((~ilf_type(C, set_type)) | (subset(B, C) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B)))))))), (![C: $i] : (ilf_type(C, set_type) => (subset(B, C) <=> ![D: $i] : (ilf_type(D, set_type) => (member(D, B) => member(D, C))))) <=> ![C: $i] : ((~ilf_type(C, set_type)) | (subset(B, C) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))))), ((ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (subset(B, C) <=> ![D: $i] : (ilf_type(D, set_type) => (member(D, B) => member(D, C)))))) <=> (ilf_type(B, set_type) => ![C: $i] : ((~ilf_type(C, set_type)) | (subset(B, C) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B)))))))), rewrite((ilf_type(B, set_type) => ![C: $i] : ((~ilf_type(C, set_type)) | (subset(B, C) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B)))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (subset(B, C) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))))), ((ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (subset(B, C) <=> ![D: $i] : (ilf_type(D, set_type) => (member(D, B) => member(D, C)))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (subset(B, C) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))))))),
% 1.33/1.11 inference(bind,[status(th)],[])).
% 1.33/1.11 tff(195,plain,
% 1.33/1.11 (![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (subset(B, C) <=> ![D: $i] : (ilf_type(D, set_type) => (member(D, B) => member(D, C)))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (subset(B, C) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))))),
% 1.33/1.11 inference(quant_intro,[status(thm)],[194])).
% 1.33/1.11 tff(196,axiom,(![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, set_type) => (subset(B, C) <=> ![D: $i] : (ilf_type(D, set_type) => (member(D, B) => member(D, C))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p5')).
% 1.33/1.11 tff(197,plain,
% 1.33/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (subset(B, C) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))))),
% 1.33/1.11 inference(modus_ponens,[status(thm)],[196, 195])).
% 1.33/1.11 tff(198,plain,
% 1.33/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (subset(B, C) <=> ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))))),
% 1.33/1.11 inference(modus_ponens,[status(thm)],[197, 193])).
% 1.33/1.11 tff(199,plain,(
% 1.33/1.11 ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B)))) & (subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))),
% 1.33/1.11 inference(skolemize,[status(sab)],[198])).
% 1.33/1.11 tff(200,plain,
% 1.33/1.11 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))),
% 1.33/1.11 inference(modus_ponens,[status(thm)],[199, 192])).
% 1.33/1.12 tff(201,plain,
% 1.33/1.12 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))),
% 1.33/1.12 inference(modus_ponens,[status(thm)],[200, 190])).
% 1.33/1.12 tff(202,plain,
% 1.33/1.12 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))) | ((~ilf_type(B!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10)))) | subset(B!10, C)))))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))) | (~ilf_type(B!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10)))) | subset(B!10, C)))))))),
% 1.33/1.12 inference(rewrite,[status(thm)],[])).
% 1.33/1.12 tff(203,plain,
% 1.33/1.12 (((~ilf_type(B!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(subset(B!10, C) | (~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10)))))))))) <=> ((~ilf_type(B!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10)))) | subset(B!10, C)))))))),
% 1.33/1.12 inference(rewrite,[status(thm)],[])).
% 1.33/1.12 tff(204,plain,
% 1.33/1.12 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))) | ((~ilf_type(B!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(subset(B!10, C) | (~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10))))))))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))) | ((~ilf_type(B!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10)))) | subset(B!10, C))))))))),
% 1.33/1.12 inference(monotonicity,[status(thm)],[203])).
% 1.33/1.12 tff(205,plain,
% 1.33/1.12 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))) | ((~ilf_type(B!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(subset(B!10, C) | (~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10))))))))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))) | (~ilf_type(B!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10)))) | subset(B!10, C)))))))),
% 1.33/1.12 inference(transitivity,[status(thm)],[204, 202])).
% 1.33/1.12 tff(206,plain,
% 1.33/1.12 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))) | ((~ilf_type(B!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~(subset(B!10, C) | (~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10))))))))))),
% 1.33/1.12 inference(quant_inst,[status(thm)],[])).
% 1.33/1.12 tff(207,plain,
% 1.33/1.12 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B))))) | (~(subset(B, C) | (~(member(tptp_fun_D_3(C, B), C) | (~ilf_type(tptp_fun_D_3(C, B), set_type)) | (~member(tptp_fun_D_3(C, B), B))))))))))) | (~ilf_type(B!10, set_type)) | ![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10)))) | subset(B!10, C))))))),
% 1.33/1.12 inference(modus_ponens,[status(thm)],[206, 205])).
% 1.33/1.12 tff(208,plain,
% 1.33/1.12 (![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10)))) | subset(B!10, C))))))),
% 1.33/1.12 inference(unit_resolution,[status(thm)],[207, 201, 41])).
% 1.33/1.12 tff(209,plain,
% 1.33/1.12 (((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10)))) | subset(B!10, C))))))) | ((~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~subset(B!10, cross_product(C!11, D!12))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | subset(B!10, cross_product(C!11, D!12)))))))) <=> ((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10)))) | subset(B!10, C))))))) | (~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~subset(B!10, cross_product(C!11, D!12))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | subset(B!10, cross_product(C!11, D!12)))))))),
% 1.33/1.12 inference(rewrite,[status(thm)],[])).
% 1.33/1.12 tff(210,plain,
% 1.33/1.12 (((~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~subset(B!10, cross_product(C!11, D!12))) | ![D: $i] : (member(D, cross_product(C!11, D!12)) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | subset(B!10, cross_product(C!11, D!12))))))) <=> ((~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~subset(B!10, cross_product(C!11, D!12))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | subset(B!10, cross_product(C!11, D!12)))))))),
% 1.33/1.12 inference(rewrite,[status(thm)],[])).
% 1.33/1.12 tff(211,plain,
% 1.33/1.12 (((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10)))) | subset(B!10, C))))))) | ((~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~subset(B!10, cross_product(C!11, D!12))) | ![D: $i] : (member(D, cross_product(C!11, D!12)) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | subset(B!10, cross_product(C!11, D!12)))))))) <=> ((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10)))) | subset(B!10, C))))))) | ((~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~subset(B!10, cross_product(C!11, D!12))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | subset(B!10, cross_product(C!11, D!12))))))))),
% 1.33/1.12 inference(monotonicity,[status(thm)],[210])).
% 1.33/1.12 tff(212,plain,
% 1.33/1.12 (((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10)))) | subset(B!10, C))))))) | ((~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~subset(B!10, cross_product(C!11, D!12))) | ![D: $i] : (member(D, cross_product(C!11, D!12)) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | subset(B!10, cross_product(C!11, D!12)))))))) <=> ((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10)))) | subset(B!10, C))))))) | (~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~subset(B!10, cross_product(C!11, D!12))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | subset(B!10, cross_product(C!11, D!12)))))))),
% 1.33/1.12 inference(transitivity,[status(thm)],[211, 209])).
% 1.33/1.12 tff(213,plain,
% 1.33/1.12 ((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10)))) | subset(B!10, C))))))) | ((~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~subset(B!10, cross_product(C!11, D!12))) | ![D: $i] : (member(D, cross_product(C!11, D!12)) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | subset(B!10, cross_product(C!11, D!12)))))))),
% 1.33/1.12 inference(quant_inst,[status(thm)],[])).
% 1.33/1.12 tff(214,plain,
% 1.33/1.12 ((~![C: $i] : ((~ilf_type(C, set_type)) | (~((~((~subset(B!10, C)) | ![D: $i] : (member(D, C) | (~ilf_type(D, set_type)) | (~member(D, B!10))))) | (~((~(member(tptp_fun_D_3(C, B!10), C) | (~ilf_type(tptp_fun_D_3(C, B!10), set_type)) | (~member(tptp_fun_D_3(C, B!10), B!10)))) | subset(B!10, C))))))) | (~ilf_type(cross_product(C!11, D!12), set_type)) | (~((~((~subset(B!10, cross_product(C!11, D!12))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | subset(B!10, cross_product(C!11, D!12))))))),
% 1.33/1.12 inference(modus_ponens,[status(thm)],[213, 212])).
% 1.33/1.12 tff(215,plain,
% 1.33/1.12 (~((~((~subset(B!10, cross_product(C!11, D!12))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | subset(B!10, cross_product(C!11, D!12)))))),
% 1.33/1.12 inference(unit_resolution,[status(thm)],[214, 208, 40])).
% 1.33/1.12 tff(216,plain,
% 1.33/1.12 (((~((~subset(B!10, cross_product(C!11, D!12))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | (~((~(member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)))) | subset(B!10, cross_product(C!11, D!12))))) | ((~subset(B!10, cross_product(C!11, D!12))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))),
% 1.33/1.12 inference(tautology,[status(thm)],[])).
% 1.33/1.12 tff(217,plain,
% 1.33/1.12 ((~subset(B!10, cross_product(C!11, D!12))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12)))),
% 1.33/1.12 inference(unit_resolution,[status(thm)],[216, 215])).
% 1.33/1.12 tff(218,plain,
% 1.33/1.12 (subset(B!10, cross_product(C!11, D!12))),
% 1.33/1.12 inference(or_elim,[status(thm)],[35])).
% 1.33/1.12 tff(219,plain,
% 1.33/1.12 ((~((~subset(B!10, cross_product(C!11, D!12))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | (~subset(B!10, cross_product(C!11, D!12))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12)))),
% 1.33/1.12 inference(tautology,[status(thm)],[])).
% 1.33/1.12 tff(220,plain,
% 1.33/1.12 ((~((~subset(B!10, cross_product(C!11, D!12))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12))))) | ![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12)))),
% 1.33/1.12 inference(unit_resolution,[status(thm)],[219, 218])).
% 1.33/1.12 tff(221,plain,
% 1.33/1.12 (![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12)))),
% 1.33/1.12 inference(unit_resolution,[status(thm)],[220, 217])).
% 1.33/1.12 tff(222,plain,
% 1.33/1.12 (((~![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12)))) | ((~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)) | member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)))) <=> ((~![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12)))) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)) | member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)))),
% 1.33/1.12 inference(rewrite,[status(thm)],[])).
% 1.33/1.12 tff(223,plain,
% 1.33/1.12 ((~![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12)))) | ((~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)) | member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12)))),
% 1.33/1.12 inference(quant_inst,[status(thm)],[])).
% 1.33/1.12 tff(224,plain,
% 1.33/1.12 ((~![D: $i] : ((~ilf_type(D, set_type)) | (~member(D, B!10)) | member(D, cross_product(C!11, D!12)))) | (~ilf_type(tptp_fun_D_3(cross_product(C!11, D!12), B!10), set_type)) | (~member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), B!10)) | member(tptp_fun_D_3(cross_product(C!11, D!12), B!10), cross_product(C!11, D!12))),
% 1.33/1.12 inference(modus_ponens,[status(thm)],[223, 222])).
% 1.33/1.12 tff(225,plain,
% 1.33/1.12 ($false),
% 1.33/1.12 inference(unit_resolution,[status(thm)],[224, 221, 185, 183, 181])).
% 1.33/1.12 % SZS output end Proof
%------------------------------------------------------------------------------