TSTP Solution File: SET658+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET658+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 05:07:32 EDT 2022
% Result : Theorem 0.48s 0.69s
% Output : Proof 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET658+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n029.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Sep 3 07:20:30 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.48/0.69 % SZS status Theorem
% 0.48/0.69 % SZS output start Proof
% 0.48/0.69 tff(subset_type, type, (
% 0.48/0.69 subset: ( $i * $i ) > $o)).
% 0.48/0.69 tff(domain_of_type, type, (
% 0.48/0.69 domain_of: $i > $i)).
% 0.48/0.69 tff(tptp_fun_B_11_type, type, (
% 0.48/0.69 tptp_fun_B_11: $i)).
% 0.48/0.69 tff(ilf_type_type, type, (
% 0.48/0.69 ilf_type: ( $i * $i ) > $o)).
% 0.48/0.69 tff(relation_type_type, type, (
% 0.48/0.69 relation_type: ( $i * $i ) > $i)).
% 0.48/0.69 tff(range_of_type, type, (
% 0.48/0.69 range_of: $i > $i)).
% 0.48/0.69 tff(binary_relation_type_type, type, (
% 0.48/0.69 binary_relation_type: $i)).
% 0.48/0.69 tff(set_type_type, type, (
% 0.48/0.69 set_type: $i)).
% 0.48/0.69 tff(1,plain,
% 0.48/0.69 ((~![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(B, relation_type(domain_of(B), range_of(B))))) <=> (~![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(B, relation_type(domain_of(B), range_of(B)))))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(2,plain,
% 0.48/0.69 ((~![B: $i] : (ilf_type(B, binary_relation_type) => ilf_type(B, relation_type(domain_of(B), range_of(B))))) <=> (~![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(B, relation_type(domain_of(B), range_of(B)))))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(3,axiom,(~![B: $i] : (ilf_type(B, binary_relation_type) => ilf_type(B, relation_type(domain_of(B), range_of(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_relset_1_20')).
% 0.48/0.69 tff(4,plain,
% 0.48/0.69 (~![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(B, relation_type(domain_of(B), range_of(B))))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.48/0.69 tff(5,plain,
% 0.48/0.69 (~![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(B, relation_type(domain_of(B), range_of(B))))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.48/0.69 tff(6,plain,
% 0.48/0.69 (~![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(B, relation_type(domain_of(B), range_of(B))))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.48/0.69 tff(7,plain,
% 0.48/0.69 (~![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(B, relation_type(domain_of(B), range_of(B))))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.48/0.69 tff(8,plain,
% 0.48/0.69 (~![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(B, relation_type(domain_of(B), range_of(B))))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.48/0.69 tff(9,plain,
% 0.48/0.69 (~![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(B, relation_type(domain_of(B), range_of(B))))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.48/0.69 tff(10,plain,
% 0.48/0.69 (~![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(B, relation_type(domain_of(B), range_of(B))))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.48/0.69 tff(11,plain,(
% 0.48/0.69 ~((~ilf_type(B!11, binary_relation_type)) | ilf_type(B!11, relation_type(domain_of(B!11), range_of(B!11))))),
% 0.48/0.69 inference(skolemize,[status(sab)],[10])).
% 0.48/0.69 tff(12,plain,
% 0.48/0.69 (ilf_type(B!11, binary_relation_type)),
% 0.48/0.69 inference(or_elim,[status(thm)],[11])).
% 0.48/0.69 tff(13,plain,
% 0.48/0.69 (^[B: $i] : refl(((~ilf_type(B, binary_relation_type)) | ilf_type(domain_of(B), set_type)) <=> ((~ilf_type(B, binary_relation_type)) | ilf_type(domain_of(B), set_type)))),
% 0.48/0.69 inference(bind,[status(th)],[])).
% 0.48/0.69 tff(14,plain,
% 0.48/0.69 (![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(domain_of(B), set_type)) <=> ![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(domain_of(B), set_type))),
% 0.48/0.69 inference(quant_intro,[status(thm)],[13])).
% 0.48/0.69 tff(15,plain,
% 0.48/0.69 (![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(domain_of(B), set_type)) <=> ![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(domain_of(B), set_type))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(16,plain,
% 0.48/0.69 (^[B: $i] : rewrite((ilf_type(B, binary_relation_type) => ilf_type(domain_of(B), set_type)) <=> ((~ilf_type(B, binary_relation_type)) | ilf_type(domain_of(B), set_type)))),
% 0.48/0.69 inference(bind,[status(th)],[])).
% 0.48/0.69 tff(17,plain,
% 0.48/0.69 (![B: $i] : (ilf_type(B, binary_relation_type) => ilf_type(domain_of(B), set_type)) <=> ![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(domain_of(B), set_type))),
% 0.48/0.69 inference(quant_intro,[status(thm)],[16])).
% 0.48/0.69 tff(18,axiom,(![B: $i] : (ilf_type(B, binary_relation_type) => ilf_type(domain_of(B), set_type))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3')).
% 0.48/0.69 tff(19,plain,
% 0.48/0.69 (![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(domain_of(B), set_type))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.48/0.69 tff(20,plain,
% 0.48/0.69 (![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(domain_of(B), set_type))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.48/0.69 tff(21,plain,(
% 0.48/0.69 ![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(domain_of(B), set_type))),
% 0.48/0.69 inference(skolemize,[status(sab)],[20])).
% 0.48/0.69 tff(22,plain,
% 0.48/0.69 (![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(domain_of(B), set_type))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.48/0.69 tff(23,plain,
% 0.48/0.69 (((~![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(domain_of(B), set_type))) | ((~ilf_type(B!11, binary_relation_type)) | ilf_type(domain_of(B!11), set_type))) <=> ((~![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(domain_of(B), set_type))) | (~ilf_type(B!11, binary_relation_type)) | ilf_type(domain_of(B!11), set_type))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(24,plain,
% 0.48/0.69 ((~![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(domain_of(B), set_type))) | ((~ilf_type(B!11, binary_relation_type)) | ilf_type(domain_of(B!11), set_type))),
% 0.48/0.69 inference(quant_inst,[status(thm)],[])).
% 0.48/0.69 tff(25,plain,
% 0.48/0.69 ((~![B: $i] : ((~ilf_type(B, binary_relation_type)) | ilf_type(domain_of(B), set_type))) | (~ilf_type(B!11, binary_relation_type)) | ilf_type(domain_of(B!11), set_type)),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.48/0.69 tff(26,plain,
% 0.48/0.69 (ilf_type(domain_of(B!11), set_type)),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[25, 22, 12])).
% 0.48/0.69 tff(27,plain,
% 0.48/0.69 (^[B: $i] : refl(((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type)))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type)))))),
% 0.48/0.69 inference(bind,[status(th)],[])).
% 0.48/0.69 tff(28,plain,
% 0.48/0.69 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type)))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))),
% 0.48/0.69 inference(quant_intro,[status(thm)],[27])).
% 0.48/0.69 tff(29,plain,
% 0.48/0.69 (^[B: $i] : rewrite(((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type)))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type)))))),
% 0.48/0.69 inference(bind,[status(th)],[])).
% 0.48/0.69 tff(30,plain,
% 0.48/0.69 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type)))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))),
% 0.48/0.69 inference(quant_intro,[status(thm)],[29])).
% 0.48/0.69 tff(31,plain,
% 0.48/0.69 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type)))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))),
% 0.48/0.69 inference(transitivity,[status(thm)],[30, 28])).
% 0.48/0.69 tff(32,plain,
% 0.48/0.69 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type)))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(33,plain,
% 0.48/0.69 (^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((subset(domain_of(C), B) => ilf_type(C, relation_type(B, range_of(C)))) <=> ((~subset(domain_of(C), B)) | ilf_type(C, relation_type(B, range_of(C))))), ((ilf_type(C, binary_relation_type) => (subset(domain_of(C), B) => ilf_type(C, relation_type(B, range_of(C))))) <=> (ilf_type(C, binary_relation_type) => ((~subset(domain_of(C), B)) | ilf_type(C, relation_type(B, range_of(C))))))), rewrite((ilf_type(C, binary_relation_type) => ((~subset(domain_of(C), B)) | ilf_type(C, relation_type(B, range_of(C))))) <=> (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type)))), ((ilf_type(C, binary_relation_type) => (subset(domain_of(C), B) => ilf_type(C, relation_type(B, range_of(C))))) <=> (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type)))))), (![C: $i] : (ilf_type(C, binary_relation_type) => (subset(domain_of(C), B) => ilf_type(C, relation_type(B, range_of(C))))) <=> ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))), ((ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, binary_relation_type) => (subset(domain_of(C), B) => ilf_type(C, relation_type(B, range_of(C)))))) <=> (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type)))))), rewrite((ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type)))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))), ((ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, binary_relation_type) => (subset(domain_of(C), B) => ilf_type(C, relation_type(B, range_of(C)))))) <=> ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))))),
% 0.48/0.69 inference(bind,[status(th)],[])).
% 0.48/0.69 tff(34,plain,
% 0.48/0.69 (![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, binary_relation_type) => (subset(domain_of(C), B) => ilf_type(C, relation_type(B, range_of(C)))))) <=> ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))),
% 0.48/0.69 inference(quant_intro,[status(thm)],[33])).
% 0.48/0.69 tff(35,axiom,(![B: $i] : (ilf_type(B, set_type) => ![C: $i] : (ilf_type(C, binary_relation_type) => (subset(domain_of(C), B) => ilf_type(C, relation_type(B, range_of(C))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p1')).
% 0.48/0.69 tff(36,plain,
% 0.48/0.69 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.48/0.69 tff(37,plain,
% 0.48/0.69 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.48/0.69 tff(38,plain,(
% 0.48/0.69 ![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))),
% 0.48/0.69 inference(skolemize,[status(sab)],[37])).
% 0.48/0.69 tff(39,plain,
% 0.48/0.69 (![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.48/0.69 tff(40,plain,
% 0.48/0.69 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))) | ((~ilf_type(domain_of(B!11), set_type)) | ![C: $i] : ((~ilf_type(C, binary_relation_type)) | ilf_type(C, relation_type(domain_of(B!11), range_of(C))) | (~subset(domain_of(C), domain_of(B!11)))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))) | (~ilf_type(domain_of(B!11), set_type)) | ![C: $i] : ((~ilf_type(C, binary_relation_type)) | ilf_type(C, relation_type(domain_of(B!11), range_of(C))) | (~subset(domain_of(C), domain_of(B!11)))))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(41,plain,
% 0.48/0.69 (((~ilf_type(domain_of(B!11), set_type)) | ![C: $i] : (ilf_type(C, relation_type(domain_of(B!11), range_of(C))) | (~subset(domain_of(C), domain_of(B!11))) | (~ilf_type(C, binary_relation_type)))) <=> ((~ilf_type(domain_of(B!11), set_type)) | ![C: $i] : ((~ilf_type(C, binary_relation_type)) | ilf_type(C, relation_type(domain_of(B!11), range_of(C))) | (~subset(domain_of(C), domain_of(B!11)))))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(42,plain,
% 0.48/0.69 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))) | ((~ilf_type(domain_of(B!11), set_type)) | ![C: $i] : (ilf_type(C, relation_type(domain_of(B!11), range_of(C))) | (~subset(domain_of(C), domain_of(B!11))) | (~ilf_type(C, binary_relation_type))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))) | ((~ilf_type(domain_of(B!11), set_type)) | ![C: $i] : ((~ilf_type(C, binary_relation_type)) | ilf_type(C, relation_type(domain_of(B!11), range_of(C))) | (~subset(domain_of(C), domain_of(B!11))))))),
% 0.48/0.69 inference(monotonicity,[status(thm)],[41])).
% 0.48/0.69 tff(43,plain,
% 0.48/0.69 (((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))) | ((~ilf_type(domain_of(B!11), set_type)) | ![C: $i] : (ilf_type(C, relation_type(domain_of(B!11), range_of(C))) | (~subset(domain_of(C), domain_of(B!11))) | (~ilf_type(C, binary_relation_type))))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))) | (~ilf_type(domain_of(B!11), set_type)) | ![C: $i] : ((~ilf_type(C, binary_relation_type)) | ilf_type(C, relation_type(domain_of(B!11), range_of(C))) | (~subset(domain_of(C), domain_of(B!11)))))),
% 0.48/0.69 inference(transitivity,[status(thm)],[42, 40])).
% 0.48/0.69 tff(44,plain,
% 0.48/0.69 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))) | ((~ilf_type(domain_of(B!11), set_type)) | ![C: $i] : (ilf_type(C, relation_type(domain_of(B!11), range_of(C))) | (~subset(domain_of(C), domain_of(B!11))) | (~ilf_type(C, binary_relation_type))))),
% 0.48/0.69 inference(quant_inst,[status(thm)],[])).
% 0.48/0.69 tff(45,plain,
% 0.48/0.69 ((~![B: $i] : ((~ilf_type(B, set_type)) | ![C: $i] : (ilf_type(C, relation_type(B, range_of(C))) | (~subset(domain_of(C), B)) | (~ilf_type(C, binary_relation_type))))) | (~ilf_type(domain_of(B!11), set_type)) | ![C: $i] : ((~ilf_type(C, binary_relation_type)) | ilf_type(C, relation_type(domain_of(B!11), range_of(C))) | (~subset(domain_of(C), domain_of(B!11))))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.48/0.69 tff(46,plain,
% 0.48/0.69 (![C: $i] : ((~ilf_type(C, binary_relation_type)) | ilf_type(C, relation_type(domain_of(B!11), range_of(C))) | (~subset(domain_of(C), domain_of(B!11))))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[45, 39, 26])).
% 0.48/0.69 tff(47,plain,
% 0.48/0.69 (^[B: $i] : refl(((~ilf_type(B, set_type)) | subset(B, B)) <=> ((~ilf_type(B, set_type)) | subset(B, B)))),
% 0.48/0.69 inference(bind,[status(th)],[])).
% 0.48/0.69 tff(48,plain,
% 0.48/0.69 (![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B)) <=> ![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))),
% 0.48/0.69 inference(quant_intro,[status(thm)],[47])).
% 0.48/0.69 tff(49,plain,
% 0.48/0.69 (![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B)) <=> ![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.70 tff(50,plain,
% 0.48/0.70 (^[B: $i] : rewrite((ilf_type(B, set_type) => subset(B, B)) <=> ((~ilf_type(B, set_type)) | subset(B, B)))),
% 0.48/0.70 inference(bind,[status(th)],[])).
% 0.48/0.70 tff(51,plain,
% 0.48/0.70 (![B: $i] : (ilf_type(B, set_type) => subset(B, B)) <=> ![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))),
% 0.48/0.70 inference(quant_intro,[status(thm)],[50])).
% 0.48/0.70 tff(52,axiom,(![B: $i] : (ilf_type(B, set_type) => subset(B, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p15')).
% 0.48/0.70 tff(53,plain,
% 0.48/0.70 (![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))),
% 0.48/0.70 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.48/0.70 tff(54,plain,
% 0.48/0.70 (![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))),
% 0.48/0.70 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.48/0.70 tff(55,plain,(
% 0.48/0.70 ![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))),
% 0.48/0.70 inference(skolemize,[status(sab)],[54])).
% 0.48/0.70 tff(56,plain,
% 0.48/0.70 (![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))),
% 0.48/0.70 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.48/0.70 tff(57,plain,
% 0.48/0.70 (((~![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))) | ((~ilf_type(domain_of(B!11), set_type)) | subset(domain_of(B!11), domain_of(B!11)))) <=> ((~![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))) | (~ilf_type(domain_of(B!11), set_type)) | subset(domain_of(B!11), domain_of(B!11)))),
% 0.48/0.70 inference(rewrite,[status(thm)],[])).
% 0.48/0.70 tff(58,plain,
% 0.48/0.70 ((~![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))) | ((~ilf_type(domain_of(B!11), set_type)) | subset(domain_of(B!11), domain_of(B!11)))),
% 0.48/0.70 inference(quant_inst,[status(thm)],[])).
% 0.48/0.70 tff(59,plain,
% 0.48/0.70 ((~![B: $i] : ((~ilf_type(B, set_type)) | subset(B, B))) | (~ilf_type(domain_of(B!11), set_type)) | subset(domain_of(B!11), domain_of(B!11))),
% 0.48/0.70 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.48/0.70 tff(60,plain,
% 0.48/0.70 (subset(domain_of(B!11), domain_of(B!11))),
% 0.48/0.70 inference(unit_resolution,[status(thm)],[59, 56, 26])).
% 0.48/0.70 tff(61,plain,
% 0.48/0.70 (~ilf_type(B!11, relation_type(domain_of(B!11), range_of(B!11)))),
% 0.48/0.70 inference(or_elim,[status(thm)],[11])).
% 0.48/0.70 tff(62,plain,
% 0.48/0.70 (((~![C: $i] : ((~ilf_type(C, binary_relation_type)) | ilf_type(C, relation_type(domain_of(B!11), range_of(C))) | (~subset(domain_of(C), domain_of(B!11))))) | ((~ilf_type(B!11, binary_relation_type)) | ilf_type(B!11, relation_type(domain_of(B!11), range_of(B!11))) | (~subset(domain_of(B!11), domain_of(B!11))))) <=> ((~![C: $i] : ((~ilf_type(C, binary_relation_type)) | ilf_type(C, relation_type(domain_of(B!11), range_of(C))) | (~subset(domain_of(C), domain_of(B!11))))) | (~ilf_type(B!11, binary_relation_type)) | ilf_type(B!11, relation_type(domain_of(B!11), range_of(B!11))) | (~subset(domain_of(B!11), domain_of(B!11))))),
% 0.48/0.70 inference(rewrite,[status(thm)],[])).
% 0.48/0.70 tff(63,plain,
% 0.48/0.70 ((~![C: $i] : ((~ilf_type(C, binary_relation_type)) | ilf_type(C, relation_type(domain_of(B!11), range_of(C))) | (~subset(domain_of(C), domain_of(B!11))))) | ((~ilf_type(B!11, binary_relation_type)) | ilf_type(B!11, relation_type(domain_of(B!11), range_of(B!11))) | (~subset(domain_of(B!11), domain_of(B!11))))),
% 0.48/0.70 inference(quant_inst,[status(thm)],[])).
% 0.48/0.70 tff(64,plain,
% 0.48/0.70 ((~![C: $i] : ((~ilf_type(C, binary_relation_type)) | ilf_type(C, relation_type(domain_of(B!11), range_of(C))) | (~subset(domain_of(C), domain_of(B!11))))) | (~ilf_type(B!11, binary_relation_type)) | ilf_type(B!11, relation_type(domain_of(B!11), range_of(B!11))) | (~subset(domain_of(B!11), domain_of(B!11)))),
% 0.48/0.70 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.48/0.70 tff(65,plain,
% 0.48/0.70 ($false),
% 0.48/0.70 inference(unit_resolution,[status(thm)],[64, 12, 61, 60, 46])).
% 0.48/0.70 % SZS output end Proof
%------------------------------------------------------------------------------