%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SEU219+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 12:45:30 PM UTC 2026
% Result : Theorem 0.19s 0.47s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU219+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.38 % Computer : n005.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Mon Sep 28 04:07:32 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.47 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 0.19/0.47
% 0.19/0.47 % SZS status Theorem
% 0.19/0.47
% 0.19/0.47 % SZS output start Proof
% 0.19/0.47 Axiom 1 (t55_funct_1): relation(a) = true.
% 0.19/0.47 Axiom 2 (t55_funct_1_1): function(a) = true.
% 0.19/0.47 Axiom 3 (t55_funct_1_2): one_to_one(a) = true.
% 0.19/0.47 Axiom 4 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.19/0.47 Axiom 5 (t37_relat_1_1): ifeq2(relation(X), true, relation_rng(relation_inverse(X)), relation_dom(X)) = relation_dom(X).
% 0.19/0.47 Axiom 6 (t37_relat_1): ifeq2(relation(X), true, relation_dom(relation_inverse(X)), relation_rng(X)) = relation_rng(X).
% 0.19/0.47 Axiom 7 (d9_funct_1): ifeq2(one_to_one(X), true, ifeq2(function(X), true, ifeq2(relation(X), true, function_inverse(X), relation_inverse(X)), relation_inverse(X)), relation_inverse(X)) = relation_inverse(X).
% 0.19/0.47
% 0.19/0.47 Lemma 8: function_inverse(a) = relation_inverse(a).
% 0.19/0.47 Proof:
% 0.19/0.47 function_inverse(a)
% 0.19/0.47 = { by axiom 4 (ifeq_axiom) R->L }
% 0.19/0.47 ifeq2(true, true, function_inverse(a), relation_inverse(a))
% 0.19/0.47 = { by axiom 4 (ifeq_axiom) R->L }
% 0.19/0.47 ifeq2(true, true, ifeq2(true, true, function_inverse(a), relation_inverse(a)), relation_inverse(a))
% 0.19/0.47 = { by axiom 2 (t55_funct_1_1) R->L }
% 0.19/0.47 ifeq2(function(a), true, ifeq2(true, true, function_inverse(a), relation_inverse(a)), relation_inverse(a))
% 0.19/0.47 = { by axiom 4 (ifeq_axiom) R->L }
% 0.19/0.47 ifeq2(true, true, ifeq2(function(a), true, ifeq2(true, true, function_inverse(a), relation_inverse(a)), relation_inverse(a)), relation_inverse(a))
% 0.19/0.47 = { by axiom 3 (t55_funct_1_2) R->L }
% 0.19/0.47 ifeq2(one_to_one(a), true, ifeq2(function(a), true, ifeq2(true, true, function_inverse(a), relation_inverse(a)), relation_inverse(a)), relation_inverse(a))
% 0.19/0.47 = { by axiom 1 (t55_funct_1) R->L }
% 0.19/0.47 ifeq2(one_to_one(a), true, ifeq2(function(a), true, ifeq2(relation(a), true, function_inverse(a), relation_inverse(a)), relation_inverse(a)), relation_inverse(a))
% 0.19/0.47 = { by axiom 7 (d9_funct_1) }
% 0.19/0.47 relation_inverse(a)
% 0.19/0.47
% 0.19/0.47 Goal 1 (t55_funct_1_3): tuple(relation_dom(a), relation_rng(a)) = tuple(relation_rng(function_inverse(a)), relation_dom(function_inverse(a))).
% 0.19/0.47 Proof:
% 0.19/0.47 tuple(relation_dom(a), relation_rng(a))
% 0.19/0.47 = { by axiom 5 (t37_relat_1_1) R->L }
% 0.19/0.47 tuple(ifeq2(relation(a), true, relation_rng(relation_inverse(a)), relation_dom(a)), relation_rng(a))
% 0.19/0.47 = { by axiom 1 (t55_funct_1) }
% 0.19/0.47 tuple(ifeq2(true, true, relation_rng(relation_inverse(a)), relation_dom(a)), relation_rng(a))
% 0.19/0.47 = { by axiom 4 (ifeq_axiom) }
% 0.19/0.47 tuple(relation_rng(relation_inverse(a)), relation_rng(a))
% 0.19/0.47 = { by lemma 8 R->L }
% 0.19/0.47 tuple(relation_rng(function_inverse(a)), relation_rng(a))
% 0.19/0.47 = { by axiom 6 (t37_relat_1) R->L }
% 0.19/0.47 tuple(relation_rng(function_inverse(a)), ifeq2(relation(a), true, relation_dom(relation_inverse(a)), relation_rng(a)))
% 0.19/0.47 = { by axiom 1 (t55_funct_1) }
% 0.19/0.47 tuple(relation_rng(function_inverse(a)), ifeq2(true, true, relation_dom(relation_inverse(a)), relation_rng(a)))
% 0.19/0.47 = { by axiom 4 (ifeq_axiom) }
% 0.19/0.47 tuple(relation_rng(function_inverse(a)), relation_dom(relation_inverse(a)))
% 0.19/0.47 = { by lemma 8 R->L }
% 0.19/0.47 tuple(relation_rng(function_inverse(a)), relation_dom(function_inverse(a)))
% 0.19/0.47 % SZS output end Proof
% 0.19/0.47
% 0.19/0.47 RESULT: Theorem (the conjecture is true).
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