%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ALG201+1 : TPTP v9.3.1. Released v2.7.0.
% 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 09:07:08 AM UTC 2026
% Result : Theorem 0.06s 0.26s
% Output : Proof 0.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG201+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.18 % Computer : n005.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Mon Sep 28 19:41:31 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.26 Command-line arguments: --no-flatten-goal
% 0.06/0.26
% 0.06/0.26 % SZS status Theorem
% 0.06/0.26
% 0.06/0.26 % SZS output start Proof
% 0.06/0.26 Axiom 1 (ax4_1): sorti2(u) = true.
% 0.06/0.26 Axiom 2 (ax4): op2(u, u) = u.
% 0.06/0.26 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.06/0.26 Axiom 4 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.06/0.26 Axiom 5 (co1_3): ifeq(sorti2(X), true, sorti1(j(X)), true) = true.
% 0.06/0.26 Axiom 6 (co1_4): ifeq2(sorti2(X), true, ifeq2(sorti2(Y), true, op1(j(Y), j(X)), j(op2(Y, X))), j(op2(Y, X))) = j(op2(Y, X)).
% 0.06/0.26
% 0.06/0.26 Goal 1 (ax3): tuple(op1(X, X), sorti1(X)) = tuple(X, true).
% 0.06/0.26 The goal is true when:
% 0.06/0.26 X = j(u)
% 0.06/0.26
% 0.06/0.26 Proof:
% 0.06/0.26 tuple(op1(j(u), j(u)), sorti1(j(u)))
% 0.06/0.26 = { by axiom 4 (ifeq_axiom) R->L }
% 0.06/0.26 tuple(ifeq2(true, true, op1(j(u), j(u)), j(u)), sorti1(j(u)))
% 0.06/0.26 = { by axiom 4 (ifeq_axiom) R->L }
% 0.06/0.26 tuple(ifeq2(true, true, ifeq2(true, true, op1(j(u), j(u)), j(u)), j(op2(u, u))), sorti1(j(u)))
% 0.06/0.26 = { by axiom 1 (ax4_1) R->L }
% 0.06/0.26 tuple(ifeq2(sorti2(u), true, ifeq2(true, true, op1(j(u), j(u)), j(u)), j(op2(u, u))), sorti1(j(u)))
% 0.06/0.26 = { by axiom 1 (ax4_1) R->L }
% 0.06/0.26 tuple(ifeq2(sorti2(u), true, ifeq2(sorti2(u), true, op1(j(u), j(u)), j(u)), j(op2(u, u))), sorti1(j(u)))
% 0.06/0.26 = { by axiom 2 (ax4) R->L }
% 0.06/0.26 tuple(ifeq2(sorti2(u), true, ifeq2(sorti2(u), true, op1(j(u), j(u)), j(op2(u, u))), j(op2(u, u))), sorti1(j(u)))
% 0.06/0.26 = { by axiom 6 (co1_4) }
% 0.06/0.26 tuple(j(op2(u, u)), sorti1(j(u)))
% 0.06/0.26 = { by axiom 2 (ax4) }
% 0.06/0.26 tuple(j(u), sorti1(j(u)))
% 0.06/0.26 = { by axiom 3 (ifeq_axiom) R->L }
% 0.06/0.26 tuple(j(u), ifeq(true, true, sorti1(j(u)), true))
% 0.06/0.26 = { by axiom 1 (ax4_1) R->L }
% 0.06/0.26 tuple(j(u), ifeq(sorti2(u), true, sorti1(j(u)), true))
% 0.06/0.26 = { by axiom 5 (co1_3) }
% 0.06/0.26 tuple(j(u), true)
% 0.06/0.26 % SZS output end Proof
% 0.06/0.26
% 0.06/0.26 RESULT: Theorem (the conjecture is true).
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