%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU096+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 : Sat Jun 21 05:26:53 AM UTC 2025
% Result : Theorem 0.22s 0.41s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SEU096+1 : TPTP v9.0.0. Released v3.2.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 06:03:55 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.22/0.41 % SZS status Theorem
% 0.22/0.41 % SZS output start Proof
% 0.22/0.41 tff(finite_type, type, (
% 0.22/0.41 finite: $i > $o)).
% 0.22/0.41 tff(relation_image_type, type, (
% 0.22/0.41 relation_image: ( $i * $i ) > $i)).
% 0.22/0.41 tff(relation_inverse_image_type, type, (
% 0.22/0.41 relation_inverse_image: ( $i * $i ) > $i)).
% 0.22/0.41 tff(tptp_fun_A_27_type, type, (
% 0.22/0.41 tptp_fun_A_27: $i)).
% 0.22/0.41 tff(tptp_fun_B_26_type, type, (
% 0.22/0.41 tptp_fun_B_26: $i)).
% 0.22/0.41 tff(subset_type, type, (
% 0.22/0.41 subset: ( $i * $i ) > $o)).
% 0.22/0.41 tff(relation_rng_type, type, (
% 0.22/0.41 relation_rng: $i > $i)).
% 0.22/0.41 tff(function_type, type, (
% 0.22/0.41 function: $i > $o)).
% 0.22/0.41 tff(relation_type, type, (
% 0.22/0.41 relation: $i > $o)).
% 0.22/0.41 tff(1,plain,
% 0.22/0.41 ((~![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))))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(2,plain,
% 0.22/0.41 ((~![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))))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 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/sandbox/benchmark/theBenchmark.p','t27_finset_1')).
% 0.22/0.41 tff(4,plain,
% 0.22/0.41 (~![A: $i, B: $i] : (finite(A) | (~(relation(B) & function(B))) | (~(subset(A, relation_rng(B)) & finite(relation_inverse_image(B, A)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.22/0.41 tff(5,plain,
% 0.22/0.41 (~![A: $i, B: $i] : (finite(A) | (~(relation(B) & function(B))) | (~(subset(A, relation_rng(B)) & finite(relation_inverse_image(B, A)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.22/0.41 tff(6,plain,
% 0.22/0.41 (~![A: $i, B: $i] : (finite(A) | (~(relation(B) & function(B))) | (~(subset(A, relation_rng(B)) & finite(relation_inverse_image(B, A)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.22/0.41 tff(7,plain,
% 0.22/0.41 (~![A: $i, B: $i] : (finite(A) | (~(relation(B) & function(B))) | (~(subset(A, relation_rng(B)) & finite(relation_inverse_image(B, A)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.22/0.41 tff(8,plain,(
% 0.22/0.41 ~(finite(A!27) | (~(relation(B!26) & function(B!26))) | (~(subset(A!27, relation_rng(B!26)) & finite(relation_inverse_image(B!26, A!27)))))),
% 0.22/0.41 inference(skolemize,[status(sab)],[7])).
% 0.22/0.41 tff(9,plain,
% 0.22/0.41 (subset(A!27, relation_rng(B!26)) & finite(relation_inverse_image(B!26, A!27))),
% 0.22/0.41 inference(or_elim,[status(thm)],[8])).
% 0.22/0.41 tff(10,plain,
% 0.22/0.41 (subset(A!27, relation_rng(B!26))),
% 0.22/0.41 inference(and_elim,[status(thm)],[9])).
% 0.22/0.41 tff(11,plain,
% 0.22/0.41 (relation(B!26) & function(B!26)),
% 0.22/0.41 inference(or_elim,[status(thm)],[8])).
% 0.22/0.41 tff(12,plain,
% 0.22/0.41 (function(B!26)),
% 0.22/0.41 inference(and_elim,[status(thm)],[11])).
% 0.22/0.41 tff(13,plain,
% 0.22/0.41 (relation(B!26)),
% 0.22/0.41 inference(and_elim,[status(thm)],[11])).
% 0.22/0.41 tff(14,plain,
% 0.22/0.41 (^[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))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(15,plain,
% 0.22/0.41 (![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)))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[14])).
% 0.22/0.41 tff(16,plain,
% 0.22/0.41 (^[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)))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(17,plain,
% 0.22/0.41 (![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)))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[16])).
% 0.22/0.41 tff(18,plain,
% 0.22/0.41 (![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))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(19,plain,
% 0.22/0.41 (^[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))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(20,plain,
% 0.22/0.41 (![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))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[19])).
% 0.22/0.41 tff(21,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/sandbox/benchmark/theBenchmark.p','t147_funct_1')).
% 0.22/0.41 tff(22,plain,
% 0.22/0.41 (![A: $i, B: $i] : ((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | (~(relation(B) & function(B))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.22/0.41 tff(23,plain,
% 0.22/0.41 (![A: $i, B: $i] : ((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | (~(relation(B) & function(B))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.22/0.41 tff(24,plain,(
% 0.22/0.41 ![A: $i, B: $i] : ((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | (~(relation(B) & function(B))))),
% 0.22/0.41 inference(skolemize,[status(sab)],[23])).
% 0.22/0.41 tff(25,plain,
% 0.22/0.41 (![A: $i, B: $i] : ((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | (~relation(B)) | (~function(B)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.22/0.41 tff(26,plain,
% 0.22/0.41 (![A: $i, B: $i] : ((relation_image(B, relation_inverse_image(B, A)) = A) | (~subset(A, relation_rng(B))) | (~relation(B)) | (~function(B)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[25, 15])).
% 0.22/0.42 tff(27,plain,
% 0.22/0.42 (((~![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))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(28,plain,
% 0.22/0.42 (((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))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(29,plain,
% 0.22/0.42 (((~![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)))))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[28])).
% 0.22/0.42 tff(30,plain,
% 0.22/0.42 (((~![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))))),
% 0.22/0.42 inference(transitivity,[status(thm)],[29, 27])).
% 0.22/0.42 tff(31,plain,
% 0.22/0.42 ((~![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)))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(32,plain,
% 0.22/0.42 ((~![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)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.22/0.42 tff(33,plain,
% 0.22/0.42 (relation_image(B!26, relation_inverse_image(B!26, A!27)) = A!27),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[32, 26, 13, 12, 10])).
% 0.22/0.42 tff(34,plain,
% 0.22/0.42 (finite(relation_image(B!26, relation_inverse_image(B!26, A!27))) <=> finite(A!27)),
% 0.22/0.42 inference(monotonicity,[status(thm)],[33])).
% 0.22/0.42 tff(35,plain,
% 0.22/0.42 (finite(A!27) <=> finite(relation_image(B!26, relation_inverse_image(B!26, A!27)))),
% 0.22/0.42 inference(symmetry,[status(thm)],[34])).
% 0.22/0.42 tff(36,plain,
% 0.22/0.42 ((~finite(A!27)) <=> (~finite(relation_image(B!26, relation_inverse_image(B!26, A!27))))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[35])).
% 0.22/0.42 tff(37,plain,
% 0.22/0.42 (~finite(A!27)),
% 0.22/0.42 inference(or_elim,[status(thm)],[8])).
% 0.22/0.42 tff(38,plain,
% 0.22/0.42 (~finite(relation_image(B!26, relation_inverse_image(B!26, A!27)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.22/0.42 tff(39,plain,
% 0.22/0.42 (finite(relation_inverse_image(B!26, A!27))),
% 0.22/0.42 inference(and_elim,[status(thm)],[9])).
% 0.22/0.42 tff(40,plain,
% 0.22/0.42 (^[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))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(41,plain,
% 0.22/0.42 (![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)))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[40])).
% 0.22/0.42 tff(42,plain,
% 0.22/0.42 (^[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)))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(43,plain,
% 0.22/0.42 (![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)))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[42])).
% 0.22/0.42 tff(44,plain,
% 0.22/0.42 (![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))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(45,plain,
% 0.22/0.42 (^[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))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(46,plain,
% 0.22/0.42 (![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))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[45])).
% 0.22/0.42 tff(47,axiom,(![A: $i, B: $i] : (((relation(A) & function(A)) & finite(B)) => finite(relation_image(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc13_finset_1')).
% 0.22/0.42 tff(48,plain,
% 0.22/0.42 (![A: $i, B: $i] : (finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.22/0.42 tff(49,plain,
% 0.22/0.42 (![A: $i, B: $i] : (finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.22/0.42 tff(50,plain,(
% 0.22/0.42 ![A: $i, B: $i] : (finite(relation_image(A, B)) | (~(relation(A) & function(A) & finite(B))))),
% 0.22/0.42 inference(skolemize,[status(sab)],[49])).
% 0.22/0.42 tff(51,plain,
% 0.22/0.42 (![A: $i, B: $i] : (finite(relation_image(A, B)) | (~finite(B)) | (~relation(A)) | (~function(A)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.22/0.42 tff(52,plain,
% 0.22/0.42 (![A: $i, B: $i] : (finite(relation_image(A, B)) | (~finite(B)) | (~relation(A)) | (~function(A)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[51, 41])).
% 0.22/0.42 tff(53,plain,
% 0.22/0.42 (((~![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))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(54,plain,
% 0.22/0.42 ((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))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(55,plain,
% 0.22/0.42 (((~![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)))))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[54])).
% 0.22/0.42 tff(56,plain,
% 0.22/0.42 (((~![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))))),
% 0.22/0.42 inference(transitivity,[status(thm)],[55, 53])).
% 0.22/0.42 tff(57,plain,
% 0.22/0.42 ((~![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)))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(58,plain,
% 0.22/0.42 ((~![A: $i, B: $i] : (finite(relation_image(A, B)) | (~finite(B)) | (~relation(A)) | (~function(A)))) | (~finite(relation_inverse_image(B!26, A!27))) | (~relation(B!26)) | (~function(B!26)) | finite(relation_image(B!26, relation_inverse_image(B!26, A!27)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.22/0.42 tff(59,plain,
% 0.22/0.42 (finite(relation_image(B!26, relation_inverse_image(B!26, A!27)))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[58, 52, 13, 12, 39])).
% 0.22/0.42 tff(60,plain,
% 0.22/0.42 ($false),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[59, 38])).
% 0.22/0.42 % SZS output end Proof
% 0.22/0.43 % E exiting
%------------------------------------------------------------------------------