TSTP Solution File: SEU096+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU096+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 07:27:29 EDT 2022
% Result : Theorem 0.21s 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU096+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n017.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 08:48:24 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.
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42 % SZS output start Proof
% 0.21/0.42 tff(finite_type, type, (
% 0.21/0.42 finite: $i > $o)).
% 0.21/0.42 tff(relation_image_type, type, (
% 0.21/0.42 relation_image: ( $i * $i ) > $i)).
% 0.21/0.42 tff(relation_inverse_image_type, type, (
% 0.21/0.42 relation_inverse_image: ( $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_A_27_type, type, (
% 0.21/0.42 tptp_fun_A_27: $i)).
% 0.21/0.42 tff(tptp_fun_B_26_type, type, (
% 0.21/0.42 tptp_fun_B_26: $i)).
% 0.21/0.42 tff(subset_type, type, (
% 0.21/0.42 subset: ( $i * $i ) > $o)).
% 0.21/0.42 tff(relation_rng_type, type, (
% 0.21/0.42 relation_rng: $i > $i)).
% 0.21/0.42 tff(function_type, type, (
% 0.21/0.42 function: $i > $o)).
% 0.21/0.42 tff(relation_type, type, (
% 0.21/0.42 relation: $i > $o)).
% 0.21/0.42 tff(1,plain,
% 0.21/0.42 ((~![A: $i, B: $i] : (finite(A) | (~(relation(B) & function(B))) | (~(subset(A, relation_rng(B)) & finite(relation_inverse_image(B, A)))))) <=> (~![A: $i, B: $i] : (finite(A) | (~(relation(B) & function(B))) | (~(subset(A, relation_rng(B)) & finite(relation_inverse_image(B, A))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(2,plain,
% 0.21/0.42 ((~![A: $i, B: $i] : ((relation(B) & function(B)) => ((subset(A, relation_rng(B)) & finite(relation_inverse_image(B, A))) => finite(A)))) <=> (~![A: $i, B: $i] : (finite(A) | (~(relation(B) & function(B))) | (~(subset(A, relation_rng(B)) & finite(relation_inverse_image(B, A))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(3,axiom,(~![A: $i, B: $i] : ((relation(B) & function(B)) => ((subset(A, relation_rng(B)) & finite(relation_inverse_image(B, A))) => finite(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t27_finset_1')).
% 0.21/0.42 tff(4,plain,
% 0.21/0.42 (~![A: $i, B: $i] : (finite(A) | (~(relation(B) & function(B))) | (~(subset(A, relation_rng(B)) & finite(relation_inverse_image(B, A)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.21/0.42 tff(5,plain,
% 0.21/0.42 (~![A: $i, B: $i] : (finite(A) | (~(relation(B) & function(B))) | (~(subset(A, relation_rng(B)) & finite(relation_inverse_image(B, A)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.21/0.42 tff(6,plain,
% 0.21/0.42 (~![A: $i, B: $i] : (finite(A) | (~(relation(B) & function(B))) | (~(subset(A, relation_rng(B)) & finite(relation_inverse_image(B, A)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.21/0.42 tff(7,plain,
% 0.21/0.42 (~![A: $i, B: $i] : (finite(A) | (~(relation(B) & function(B))) | (~(subset(A, relation_rng(B)) & finite(relation_inverse_image(B, A)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.21/0.42 tff(8,plain,
% 0.21/0.42 (~![A: $i, B: $i] : (finite(A) | (~(relation(B) & function(B))) | (~(subset(A, relation_rng(B)) & finite(relation_inverse_image(B, A)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.21/0.42 tff(9,plain,
% 0.21/0.42 (~![A: $i, B: $i] : (finite(A) | (~(relation(B) & function(B))) | (~(subset(A, relation_rng(B)) & finite(relation_inverse_image(B, A)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.21/0.42 tff(10,plain,
% 0.21/0.42 (~![A: $i, B: $i] : (finite(A) | (~(relation(B) & function(B))) | (~(subset(A, relation_rng(B)) & finite(relation_inverse_image(B, A)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.21/0.42 tff(11,plain,(
% 0.21/0.42 ~(finite(A!27) | (~(relation(B!26) & function(B!26))) | (~(subset(A!27, relation_rng(B!26)) & finite(relation_inverse_image(B!26, A!27)))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[10])).
% 0.21/0.42 tff(12,plain,
% 0.21/0.42 (subset(A!27, relation_rng(B!26)) & finite(relation_inverse_image(B!26, A!27))),
% 0.21/0.42 inference(or_elim,[status(thm)],[11])).
% 0.21/0.42 tff(13,plain,
% 0.21/0.42 (subset(A!27, relation_rng(B!26))),
% 0.21/0.42 inference(and_elim,[status(thm)],[12])).
% 0.21/0.42 tff(14,plain,
% 0.21/0.42 (relation(B!26) & function(B!26)),
% 0.21/0.42 inference(or_elim,[status(thm)],[11])).
% 0.21/0.42 tff(15,plain,
% 0.21/0.42 (function(B!26)),
% 0.21/0.42 inference(and_elim,[status(thm)],[14])).
% 0.21/0.42 tff(16,plain,
% 0.21/0.42 (relation(B!26)),
% 0.21/0.42 inference(and_elim,[status(thm)],[14])).
% 0.21/0.42 tff(17,plain,
% 0.21/0.42 (^[A: $i, B: $i] : refl(((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | (~relation(B)) | (~function(B))) <=> ((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | (~relation(B)) | (~function(B))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(18,plain,
% 0.21/0.42 (![A: $i, B: $i] : ((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | (~relation(B)) | (~function(B))) <=> ![A: $i, B: $i] : ((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | (~relation(B)) | (~function(B)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[17])).
% 0.21/0.42 tff(19,plain,
% 0.21/0.42 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B))))), ((~(relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B))))))), rewrite((~(~((~relation(B)) | (~function(B))))) <=> ((~relation(B)) | (~function(B)))), ((~(relation(B) & function(B))) <=> ((~relation(B)) | (~function(B))))), (((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | (~(relation(B) & function(B)))) <=> ((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | ((~relation(B)) | (~function(B)))))), rewrite(((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | ((~relation(B)) | (~function(B)))) <=> ((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | (~relation(B)) | (~function(B)))), (((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | (~(relation(B) & function(B)))) <=> ((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | (~relation(B)) | (~function(B)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(20,plain,
% 0.21/0.42 (![A: $i, B: $i] : ((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | (~(relation(B) & function(B)))) <=> ![A: $i, B: $i] : ((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | (~relation(B)) | (~function(B)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[19])).
% 0.21/0.42 tff(21,plain,
% 0.21/0.42 (![A: $i, B: $i] : ((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | (~(relation(B) & function(B)))) <=> ![A: $i, B: $i] : ((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | (~(relation(B) & function(B))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(22,plain,
% 0.21/0.42 (^[A: $i, B: $i] : trans(monotonicity(rewrite((subset(A, relation_rng(B)) => (relation_image(B, relation_inverse_image(B, A)) = A)) <=> ((~subset(A, relation_rng(B))) | (relation_image(B, relation_inverse_image(B, A)) = A))), (((relation(B) & function(B)) => (subset(A, relation_rng(B)) => (relation_image(B, relation_inverse_image(B, A)) = A))) <=> ((relation(B) & function(B)) => ((~subset(A, relation_rng(B))) | (relation_image(B, relation_inverse_image(B, A)) = A))))), rewrite(((relation(B) & function(B)) => ((~subset(A, relation_rng(B))) | (relation_image(B, relation_inverse_image(B, A)) = A))) <=> ((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | (~(relation(B) & function(B))))), (((relation(B) & function(B)) => (subset(A, relation_rng(B)) => (relation_image(B, relation_inverse_image(B, A)) = A))) <=> ((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | (~(relation(B) & function(B))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(23,plain,
% 0.21/0.42 (![A: $i, B: $i] : ((relation(B) & function(B)) => (subset(A, relation_rng(B)) => (relation_image(B, relation_inverse_image(B, A)) = A))) <=> ![A: $i, B: $i] : ((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | (~(relation(B) & function(B))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[22])).
% 0.21/0.42 tff(24,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => (subset(A, relation_rng(B)) => (relation_image(B, relation_inverse_image(B, A)) = A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t147_funct_1')).
% 0.21/0.42 tff(25,plain,
% 0.21/0.42 (![A: $i, B: $i] : ((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | (~(relation(B) & function(B))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.21/0.42 tff(26,plain,
% 0.21/0.42 (![A: $i, B: $i] : ((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | (~(relation(B) & function(B))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.21/0.43 tff(27,plain,(
% 0.21/0.43 ![A: $i, B: $i] : ((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | (~(relation(B) & function(B))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[26])).
% 0.21/0.43 tff(28,plain,
% 0.21/0.43 (![A: $i, B: $i] : ((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | (~relation(B)) | (~function(B)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.21/0.43 tff(29,plain,
% 0.21/0.43 (![A: $i, B: $i] : ((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | (~relation(B)) | (~function(B)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.21/0.43 tff(30,plain,
% 0.21/0.43 (((~![A: $i, B: $i] : ((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | (~relation(B)) | (~function(B)))) | ((~relation(B!26)) | (~function(B!26)) | (relation_image(B!26, relation_inverse_image(B!26, A!27)) = A!27) | (~subset(A!27, relation_rng(B!26))))) <=> ((~![A: $i, B: $i] : ((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | (~relation(B)) | (~function(B)))) | (~relation(B!26)) | (~function(B!26)) | (relation_image(B!26, relation_inverse_image(B!26, A!27)) = A!27) | (~subset(A!27, relation_rng(B!26))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(31,plain,
% 0.21/0.43 (((relation_image(B!26, relation_inverse_image(B!26, A!27)) = A!27) | (~subset(A!27, relation_rng(B!26))) | (~relation(B!26)) | (~function(B!26))) <=> ((~relation(B!26)) | (~function(B!26)) | (relation_image(B!26, relation_inverse_image(B!26, A!27)) = A!27) | (~subset(A!27, relation_rng(B!26))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(32,plain,
% 0.21/0.43 (((~![A: $i, B: $i] : ((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | (~relation(B)) | (~function(B)))) | ((relation_image(B!26, relation_inverse_image(B!26, A!27)) = A!27) | (~subset(A!27, relation_rng(B!26))) | (~relation(B!26)) | (~function(B!26)))) <=> ((~![A: $i, B: $i] : ((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | (~relation(B)) | (~function(B)))) | ((~relation(B!26)) | (~function(B!26)) | (relation_image(B!26, relation_inverse_image(B!26, A!27)) = A!27) | (~subset(A!27, relation_rng(B!26)))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[31])).
% 0.21/0.43 tff(33,plain,
% 0.21/0.43 (((~![A: $i, B: $i] : ((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | (~relation(B)) | (~function(B)))) | ((relation_image(B!26, relation_inverse_image(B!26, A!27)) = A!27) | (~subset(A!27, relation_rng(B!26))) | (~relation(B!26)) | (~function(B!26)))) <=> ((~![A: $i, B: $i] : ((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | (~relation(B)) | (~function(B)))) | (~relation(B!26)) | (~function(B!26)) | (relation_image(B!26, relation_inverse_image(B!26, A!27)) = A!27) | (~subset(A!27, relation_rng(B!26))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[32, 30])).
% 0.21/0.43 tff(34,plain,
% 0.21/0.43 ((~![A: $i, B: $i] : ((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | (~relation(B)) | (~function(B)))) | ((relation_image(B!26, relation_inverse_image(B!26, A!27)) = A!27) | (~subset(A!27, relation_rng(B!26))) | (~relation(B!26)) | (~function(B!26)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(35,plain,
% 0.21/0.43 ((~![A: $i, B: $i] : ((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | (~relation(B)) | (~function(B)))) | (~relation(B!26)) | (~function(B!26)) | (relation_image(B!26, relation_inverse_image(B!26, A!27)) = A!27) | (~subset(A!27, relation_rng(B!26)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.21/0.43 tff(36,plain,
% 0.21/0.43 (relation_image(B!26, relation_inverse_image(B!26, A!27)) = A!27),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[35, 29, 16, 15, 13])).
% 0.21/0.43 tff(37,plain,
% 0.21/0.43 (finite(relation_image(B!26, relation_inverse_image(B!26, A!27))) <=> finite(A!27)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[36])).
% 0.21/0.43 tff(38,plain,
% 0.21/0.43 (finite(A!27) <=> finite(relation_image(B!26, relation_inverse_image(B!26, A!27)))),
% 0.21/0.43 inference(symmetry,[status(thm)],[37])).
% 0.21/0.43 tff(39,plain,
% 0.21/0.43 ((~finite(A!27)) <=> (~finite(relation_image(B!26, relation_inverse_image(B!26, A!27))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[38])).
% 0.21/0.43 tff(40,plain,
% 0.21/0.43 (~finite(A!27)),
% 0.21/0.43 inference(or_elim,[status(thm)],[11])).
% 0.21/0.43 tff(41,plain,
% 0.21/0.43 (~finite(relation_image(B!26, relation_inverse_image(B!26, A!27)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.21/0.43 tff(42,plain,
% 0.21/0.43 (finite(relation_inverse_image(B!26, A!27))),
% 0.21/0.43 inference(and_elim,[status(thm)],[12])).
% 0.21/0.43 tff(43,plain,
% 0.21/0.43 (^[A: $i, B: $i] : refl((finite(relation_image(A, B)) | (~finite(B)) | (~relation(A)) | (~function(A))) <=> (finite(relation_image(A, B)) | (~finite(B)) | (~relation(A)) | (~function(A))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(44,plain,
% 0.21/0.43 (![A: $i, B: $i] : (finite(relation_image(A, B)) | (~finite(B)) | (~relation(A)) | (~function(A))) <=> ![A: $i, B: $i] : (finite(relation_image(A, B)) | (~finite(B)) | (~relation(A)) | (~function(A)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[43])).
% 0.21/0.43 tff(45,plain,
% 0.21/0.43 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & function(A) & finite(B)) <=> (~((~finite(B)) | (~relation(A)) | (~function(A))))), ((~(relation(A) & function(A) & finite(B))) <=> (~(~((~finite(B)) | (~relation(A)) | (~function(A))))))), rewrite((~(~((~finite(B)) | (~relation(A)) | (~function(A))))) <=> ((~finite(B)) | (~relation(A)) | (~function(A)))), ((~(relation(A) & function(A) & finite(B))) <=> ((~finite(B)) | (~relation(A)) | (~function(A))))), ((finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B)))) <=> (finite(relation_image(A, B)) | ((~finite(B)) | (~relation(A)) | (~function(A)))))), rewrite((finite(relation_image(A, B)) | ((~finite(B)) | (~relation(A)) | (~function(A)))) <=> (finite(relation_image(A, B)) | (~finite(B)) | (~relation(A)) | (~function(A)))), ((finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B)))) <=> (finite(relation_image(A, B)) | (~finite(B)) | (~relation(A)) | (~function(A)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(46,plain,
% 0.21/0.43 (![A: $i, B: $i] : (finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B)))) <=> ![A: $i, B: $i] : (finite(relation_image(A, B)) | (~finite(B)) | (~relation(A)) | (~function(A)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[45])).
% 0.21/0.43 tff(47,plain,
% 0.21/0.43 (![A: $i, B: $i] : (finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B)))) <=> ![A: $i, B: $i] : (finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(48,plain,
% 0.21/0.43 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((relation(A) & function(A)) & finite(B)) <=> (relation(A) & function(A) & finite(B))), ((((relation(A) & function(A)) & finite(B)) => finite(relation_image(A, B))) <=> ((relation(A) & function(A) & finite(B)) => finite(relation_image(A, B))))), rewrite(((relation(A) & function(A) & finite(B)) => finite(relation_image(A, B))) <=> (finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B))))), ((((relation(A) & function(A)) & finite(B)) => finite(relation_image(A, B))) <=> (finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(49,plain,
% 0.21/0.43 (![A: $i, B: $i] : (((relation(A) & function(A)) & finite(B)) => finite(relation_image(A, B))) <=> ![A: $i, B: $i] : (finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[48])).
% 0.21/0.43 tff(50,axiom,(![A: $i, B: $i] : (((relation(A) & function(A)) & finite(B)) => finite(relation_image(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc13_finset_1')).
% 0.21/0.43 tff(51,plain,
% 0.21/0.43 (![A: $i, B: $i] : (finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.21/0.43 tff(52,plain,
% 0.21/0.43 (![A: $i, B: $i] : (finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.21/0.44 tff(53,plain,(
% 0.21/0.44 ![A: $i, B: $i] : (finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[52])).
% 0.21/0.44 tff(54,plain,
% 0.21/0.44 (![A: $i, B: $i] : (finite(relation_image(A, B)) | (~finite(B)) | (~relation(A)) | (~function(A)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.21/0.44 tff(55,plain,
% 0.21/0.44 (![A: $i, B: $i] : (finite(relation_image(A, B)) | (~finite(B)) | (~relation(A)) | (~function(A)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[54, 44])).
% 0.21/0.44 tff(56,plain,
% 0.21/0.44 (((~![A: $i, B: $i] : (finite(relation_image(A, B)) | (~finite(B)) | (~relation(A)) | (~function(A)))) | ((~finite(relation_inverse_image(B!26, A!27))) | (~relation(B!26)) | (~function(B!26)) | finite(relation_image(B!26, relation_inverse_image(B!26, A!27))))) <=> ((~![A: $i, B: $i] : (finite(relation_image(A, B)) | (~finite(B)) | (~relation(A)) | (~function(A)))) | (~finite(relation_inverse_image(B!26, A!27))) | (~relation(B!26)) | (~function(B!26)) | finite(relation_image(B!26, relation_inverse_image(B!26, A!27))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(57,plain,
% 0.21/0.44 ((finite(relation_image(B!26, relation_inverse_image(B!26, A!27))) | (~finite(relation_inverse_image(B!26, A!27))) | (~relation(B!26)) | (~function(B!26))) <=> ((~finite(relation_inverse_image(B!26, A!27))) | (~relation(B!26)) | (~function(B!26)) | finite(relation_image(B!26, relation_inverse_image(B!26, A!27))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(58,plain,
% 0.21/0.44 (((~![A: $i, B: $i] : (finite(relation_image(A, B)) | (~finite(B)) | (~relation(A)) | (~function(A)))) | (finite(relation_image(B!26, relation_inverse_image(B!26, A!27))) | (~finite(relation_inverse_image(B!26, A!27))) | (~relation(B!26)) | (~function(B!26)))) <=> ((~![A: $i, B: $i] : (finite(relation_image(A, B)) | (~finite(B)) | (~relation(A)) | (~function(A)))) | ((~finite(relation_inverse_image(B!26, A!27))) | (~relation(B!26)) | (~function(B!26)) | finite(relation_image(B!26, relation_inverse_image(B!26, A!27)))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[57])).
% 0.21/0.44 tff(59,plain,
% 0.21/0.44 (((~![A: $i, B: $i] : (finite(relation_image(A, B)) | (~finite(B)) | (~relation(A)) | (~function(A)))) | (finite(relation_image(B!26, relation_inverse_image(B!26, A!27))) | (~finite(relation_inverse_image(B!26, A!27))) | (~relation(B!26)) | (~function(B!26)))) <=> ((~![A: $i, B: $i] : (finite(relation_image(A, B)) | (~finite(B)) | (~relation(A)) | (~function(A)))) | (~finite(relation_inverse_image(B!26, A!27))) | (~relation(B!26)) | (~function(B!26)) | finite(relation_image(B!26, relation_inverse_image(B!26, A!27))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[58, 56])).
% 0.21/0.44 tff(60,plain,
% 0.21/0.44 ((~![A: $i, B: $i] : (finite(relation_image(A, B)) | (~finite(B)) | (~relation(A)) | (~function(A)))) | (finite(relation_image(B!26, relation_inverse_image(B!26, A!27))) | (~finite(relation_inverse_image(B!26, A!27))) | (~relation(B!26)) | (~function(B!26)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(61,plain,
% 0.21/0.44 ((~![A: $i, B: $i] : (finite(relation_image(A, B)) | (~finite(B)) | (~relation(A)) | (~function(A)))) | (~finite(relation_inverse_image(B!26, A!27))) | (~relation(B!26)) | (~function(B!26)) | finite(relation_image(B!26, relation_inverse_image(B!26, A!27)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.21/0.44 tff(62,plain,
% 0.21/0.44 (finite(relation_image(B!26, relation_inverse_image(B!26, A!27)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[61, 55, 16, 15, 42])).
% 0.21/0.44 tff(63,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[62, 41])).
% 0.21/0.44 % SZS output end Proof
%------------------------------------------------------------------------------