%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SEU303+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:45:43 PM UTC 2026
% Result : Theorem 0.10s 0.45s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU303+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n010.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 04:37:48 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.45 Command-line arguments: --flatten --complete-subsets
% 0.10/0.45
% 0.10/0.45 % SZS status Theorem
% 0.10/0.45
% 0.10/0.46 % SZS output start Proof
% 0.10/0.46 Axiom 1 (rc1_funct_1_1): function(a2) = true.
% 0.10/0.46 Axiom 2 (t26_finset_1_1): function(a) = true.
% 0.10/0.46 Axiom 3 (rc1_funct_1): relation(a2) = true.
% 0.10/0.46 Axiom 4 (t26_finset_1): relation(a) = true.
% 0.10/0.46 Axiom 5 (t26_finset_1_2): finite(relation_dom(a)) = true.
% 0.10/0.46 Axiom 6 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.10/0.46 Axiom 7 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.10/0.46 Axiom 8 (t146_relat_1): ifeq2(relation(X), true, relation_image(X, relation_dom(X)), relation_rng(X)) = relation_rng(X).
% 0.17/0.46 Axiom 9 (fc13_finset_1): ifeq(finite(X), true, ifeq(function(Y), true, ifeq(relation(Y), true, finite(relation_image(Y, X)), true), true), true) = true.
% 0.17/0.46
% 0.17/0.46 Lemma 10: relation(a2) = function(a2).
% 0.17/0.46 Proof:
% 0.17/0.46 relation(a2)
% 0.17/0.46 = { by axiom 3 (rc1_funct_1) }
% 0.17/0.46 true
% 0.17/0.46 = { by axiom 1 (rc1_funct_1_1) R->L }
% 0.17/0.46 function(a2)
% 0.17/0.46
% 0.17/0.46 Lemma 11: relation(a) = relation(a2).
% 0.17/0.46 Proof:
% 0.17/0.46 relation(a)
% 0.17/0.46 = { by axiom 4 (t26_finset_1) }
% 0.17/0.46 true
% 0.17/0.46 = { by axiom 1 (rc1_funct_1_1) R->L }
% 0.17/0.46 function(a2)
% 0.17/0.46 = { by lemma 10 R->L }
% 0.17/0.46 relation(a2)
% 0.17/0.46
% 0.17/0.46 Goal 1 (t26_finset_1_3): finite(relation_rng(a)) = true.
% 0.17/0.46 Proof:
% 0.17/0.46 finite(relation_rng(a))
% 0.17/0.46 = { by axiom 7 (ifeq_axiom) R->L }
% 0.17/0.46 ifeq(relation(a2), relation(a2), finite(relation_rng(a)), relation(a2))
% 0.17/0.46 = { by lemma 11 R->L }
% 0.17/0.46 ifeq(relation(a), relation(a2), finite(relation_rng(a)), relation(a2))
% 0.17/0.46 = { by axiom 7 (ifeq_axiom) R->L }
% 0.17/0.46 ifeq(relation(a2), relation(a2), ifeq(relation(a), relation(a2), finite(relation_rng(a)), relation(a2)), relation(a2))
% 0.17/0.46 = { by lemma 10 }
% 0.17/0.46 ifeq(function(a2), relation(a2), ifeq(relation(a), relation(a2), finite(relation_rng(a)), relation(a2)), relation(a2))
% 0.17/0.46 = { by axiom 1 (rc1_funct_1_1) }
% 0.17/0.46 ifeq(true, relation(a2), ifeq(relation(a), relation(a2), finite(relation_rng(a)), relation(a2)), relation(a2))
% 0.17/0.46 = { by axiom 2 (t26_finset_1_1) R->L }
% 0.17/0.46 ifeq(function(a), relation(a2), ifeq(relation(a), relation(a2), finite(relation_rng(a)), relation(a2)), relation(a2))
% 0.17/0.46 = { by axiom 7 (ifeq_axiom) R->L }
% 0.17/0.46 ifeq(relation(a2), relation(a2), ifeq(function(a), relation(a2), ifeq(relation(a), relation(a2), finite(relation_rng(a)), relation(a2)), relation(a2)), relation(a2))
% 0.17/0.46 = { by lemma 10 }
% 0.17/0.46 ifeq(function(a2), relation(a2), ifeq(function(a), relation(a2), ifeq(relation(a), relation(a2), finite(relation_rng(a)), relation(a2)), relation(a2)), relation(a2))
% 0.17/0.46 = { by axiom 1 (rc1_funct_1_1) }
% 0.17/0.46 ifeq(true, relation(a2), ifeq(function(a), relation(a2), ifeq(relation(a), relation(a2), finite(relation_rng(a)), relation(a2)), relation(a2)), relation(a2))
% 0.17/0.46 = { by axiom 5 (t26_finset_1_2) R->L }
% 0.17/0.46 ifeq(finite(relation_dom(a)), relation(a2), ifeq(function(a), relation(a2), ifeq(relation(a), relation(a2), finite(relation_rng(a)), relation(a2)), relation(a2)), relation(a2))
% 0.17/0.46 = { by axiom 8 (t146_relat_1) R->L }
% 0.17/0.46 ifeq(finite(relation_dom(a)), relation(a2), ifeq(function(a), relation(a2), ifeq(relation(a), relation(a2), finite(ifeq2(relation(a), true, relation_image(a, relation_dom(a)), relation_rng(a))), relation(a2)), relation(a2)), relation(a2))
% 0.17/0.46 = { by axiom 1 (rc1_funct_1_1) R->L }
% 0.17/0.46 ifeq(finite(relation_dom(a)), relation(a2), ifeq(function(a), relation(a2), ifeq(relation(a), relation(a2), finite(ifeq2(relation(a), function(a2), relation_image(a, relation_dom(a)), relation_rng(a))), relation(a2)), relation(a2)), relation(a2))
% 0.17/0.46 = { by lemma 10 R->L }
% 0.17/0.46 ifeq(finite(relation_dom(a)), relation(a2), ifeq(function(a), relation(a2), ifeq(relation(a), relation(a2), finite(ifeq2(relation(a), relation(a2), relation_image(a, relation_dom(a)), relation_rng(a))), relation(a2)), relation(a2)), relation(a2))
% 0.17/0.46 = { by lemma 11 }
% 0.17/0.46 ifeq(finite(relation_dom(a)), relation(a2), ifeq(function(a), relation(a2), ifeq(relation(a), relation(a2), finite(ifeq2(relation(a2), relation(a2), relation_image(a, relation_dom(a)), relation_rng(a))), relation(a2)), relation(a2)), relation(a2))
% 0.17/0.46 = { by axiom 6 (ifeq_axiom) }
% 0.17/0.46 ifeq(finite(relation_dom(a)), relation(a2), ifeq(function(a), relation(a2), ifeq(relation(a), relation(a2), finite(relation_image(a, relation_dom(a))), relation(a2)), relation(a2)), relation(a2))
% 0.17/0.46 = { by lemma 10 }
% 0.17/0.46 ifeq(finite(relation_dom(a)), function(a2), ifeq(function(a), relation(a2), ifeq(relation(a), relation(a2), finite(relation_image(a, relation_dom(a))), relation(a2)), relation(a2)), relation(a2))
% 0.17/0.46 = { by lemma 10 }
% 0.17/0.46 ifeq(finite(relation_dom(a)), function(a2), ifeq(function(a), function(a2), ifeq(relation(a), relation(a2), finite(relation_image(a, relation_dom(a))), relation(a2)), relation(a2)), relation(a2))
% 0.17/0.46 = { by lemma 10 }
% 0.17/0.46 ifeq(finite(relation_dom(a)), function(a2), ifeq(function(a), function(a2), ifeq(relation(a), function(a2), finite(relation_image(a, relation_dom(a))), relation(a2)), relation(a2)), relation(a2))
% 0.17/0.46 = { by lemma 10 }
% 0.17/0.46 ifeq(finite(relation_dom(a)), function(a2), ifeq(function(a), function(a2), ifeq(relation(a), function(a2), finite(relation_image(a, relation_dom(a))), function(a2)), relation(a2)), relation(a2))
% 0.17/0.46 = { by lemma 10 }
% 0.17/0.46 ifeq(finite(relation_dom(a)), function(a2), ifeq(function(a), function(a2), ifeq(relation(a), function(a2), finite(relation_image(a, relation_dom(a))), function(a2)), function(a2)), relation(a2))
% 0.17/0.46 = { by lemma 10 }
% 0.17/0.46 ifeq(finite(relation_dom(a)), function(a2), ifeq(function(a), function(a2), ifeq(relation(a), function(a2), finite(relation_image(a, relation_dom(a))), function(a2)), function(a2)), function(a2))
% 0.17/0.46 = { by axiom 1 (rc1_funct_1_1) }
% 0.17/0.46 ifeq(finite(relation_dom(a)), true, ifeq(function(a), function(a2), ifeq(relation(a), function(a2), finite(relation_image(a, relation_dom(a))), function(a2)), function(a2)), function(a2))
% 0.17/0.46 = { by axiom 1 (rc1_funct_1_1) }
% 0.17/0.46 ifeq(finite(relation_dom(a)), true, ifeq(function(a), true, ifeq(relation(a), function(a2), finite(relation_image(a, relation_dom(a))), function(a2)), function(a2)), function(a2))
% 0.17/0.46 = { by axiom 1 (rc1_funct_1_1) }
% 0.17/0.46 ifeq(finite(relation_dom(a)), true, ifeq(function(a), true, ifeq(relation(a), true, finite(relation_image(a, relation_dom(a))), function(a2)), function(a2)), function(a2))
% 0.17/0.46 = { by axiom 1 (rc1_funct_1_1) }
% 0.17/0.46 ifeq(finite(relation_dom(a)), true, ifeq(function(a), true, ifeq(relation(a), true, finite(relation_image(a, relation_dom(a))), true), function(a2)), function(a2))
% 0.17/0.46 = { by axiom 1 (rc1_funct_1_1) }
% 0.17/0.46 ifeq(finite(relation_dom(a)), true, ifeq(function(a), true, ifeq(relation(a), true, finite(relation_image(a, relation_dom(a))), true), true), function(a2))
% 0.17/0.46 = { by axiom 1 (rc1_funct_1_1) }
% 0.17/0.46 ifeq(finite(relation_dom(a)), true, ifeq(function(a), true, ifeq(relation(a), true, finite(relation_image(a, relation_dom(a))), true), true), true)
% 0.17/0.46 = { by axiom 9 (fc13_finset_1) }
% 0.17/0.46 true
% 0.17/0.46 % SZS output end Proof
% 0.17/0.46
% 0.17/0.46 RESULT: Theorem (the conjecture is true).
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