%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ALG202+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 0.07s 0.15s
% Output : Proof 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ALG202+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.02 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Mon Sep 28 19:41:33 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.15 Command-line arguments: --no-flatten-goal
% 0.07/0.15
% 0.07/0.15 % SZS status Theorem
% 0.07/0.15
% 0.07/0.15 % SZS output start Proof
% 0.07/0.15 Axiom 1 (ax4): sorti2(u) = true.
% 0.07/0.15 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.07/0.15 Axiom 3 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.07/0.15 Axiom 4 (co1_3): ifeq(sorti2(X), true, sorti1(j(X)), true) = true.
% 0.07/0.15 Axiom 5 (co1_5): ifeq2(sorti2(X), true, h(j(X)), X) = X.
% 0.07/0.15 Axiom 6 (ax3): ifeq2(sorti1(X), true, op1(X, X), X) = X.
% 0.07/0.15 Axiom 7 (co1_1): ifeq2(sorti1(X), true, ifeq2(sorti1(Y), true, op2(h(Y), h(X)), h(op1(Y, X))), h(op1(Y, X))) = h(op1(Y, X)).
% 0.07/0.15
% 0.07/0.15 Lemma 8: h(j(u)) = u.
% 0.07/0.15 Proof:
% 0.07/0.15 h(j(u))
% 0.07/0.15 = { by axiom 3 (ifeq_axiom) R->L }
% 0.07/0.15 ifeq2(true, true, h(j(u)), u)
% 0.07/0.15 = { by axiom 1 (ax4) R->L }
% 0.07/0.15 ifeq2(sorti2(u), true, h(j(u)), u)
% 0.07/0.15 = { by axiom 5 (co1_5) }
% 0.07/0.15 u
% 0.07/0.15
% 0.07/0.15 Lemma 9: op1(j(u), j(u)) = j(u).
% 0.07/0.15 Proof:
% 0.07/0.15 op1(j(u), j(u))
% 0.07/0.15 = { by axiom 3 (ifeq_axiom) R->L }
% 0.07/0.15 ifeq2(true, true, op1(j(u), j(u)), j(u))
% 0.07/0.15 = { by axiom 4 (co1_3) R->L }
% 0.07/0.15 ifeq2(ifeq(sorti2(u), true, sorti1(j(u)), true), true, op1(j(u), j(u)), j(u))
% 0.07/0.15 = { by axiom 1 (ax4) }
% 0.07/0.15 ifeq2(ifeq(true, true, sorti1(j(u)), true), true, op1(j(u), j(u)), j(u))
% 0.07/0.15 = { by axiom 2 (ifeq_axiom) }
% 0.07/0.15 ifeq2(sorti1(j(u)), true, op1(j(u), j(u)), j(u))
% 0.07/0.15 = { by axiom 6 (ax3) }
% 0.07/0.15 j(u)
% 0.07/0.15
% 0.07/0.15 Goal 1 (ax4_1): op2(u, u) = u.
% 0.07/0.15 Proof:
% 0.07/0.15 op2(u, u)
% 0.07/0.15 = { by lemma 8 R->L }
% 0.07/0.15 op2(h(j(u)), u)
% 0.07/0.15 = { by lemma 8 R->L }
% 0.07/0.15 op2(h(j(u)), h(j(u)))
% 0.07/0.15 = { by axiom 3 (ifeq_axiom) R->L }
% 0.07/0.15 ifeq2(true, true, op2(h(j(u)), h(j(u))), h(j(u)))
% 0.07/0.15 = { by axiom 3 (ifeq_axiom) R->L }
% 0.07/0.15 ifeq2(true, true, ifeq2(true, true, op2(h(j(u)), h(j(u))), h(j(u))), h(op1(j(u), j(u))))
% 0.07/0.15 = { by axiom 4 (co1_3) R->L }
% 0.07/0.15 ifeq2(ifeq(sorti2(u), true, sorti1(j(u)), true), true, ifeq2(true, true, op2(h(j(u)), h(j(u))), h(j(u))), h(op1(j(u), j(u))))
% 0.07/0.15 = { by axiom 1 (ax4) }
% 0.07/0.15 ifeq2(ifeq(true, true, sorti1(j(u)), true), true, ifeq2(true, true, op2(h(j(u)), h(j(u))), h(j(u))), h(op1(j(u), j(u))))
% 0.07/0.15 = { by axiom 2 (ifeq_axiom) }
% 0.07/0.15 ifeq2(sorti1(j(u)), true, ifeq2(true, true, op2(h(j(u)), h(j(u))), h(j(u))), h(op1(j(u), j(u))))
% 0.07/0.15 = { by axiom 4 (co1_3) R->L }
% 0.07/0.15 ifeq2(sorti1(j(u)), true, ifeq2(ifeq(sorti2(u), true, sorti1(j(u)), true), true, op2(h(j(u)), h(j(u))), h(j(u))), h(op1(j(u), j(u))))
% 0.07/0.15 = { by axiom 1 (ax4) }
% 0.07/0.15 ifeq2(sorti1(j(u)), true, ifeq2(ifeq(true, true, sorti1(j(u)), true), true, op2(h(j(u)), h(j(u))), h(j(u))), h(op1(j(u), j(u))))
% 0.07/0.15 = { by axiom 2 (ifeq_axiom) }
% 0.07/0.15 ifeq2(sorti1(j(u)), true, ifeq2(sorti1(j(u)), true, op2(h(j(u)), h(j(u))), h(j(u))), h(op1(j(u), j(u))))
% 0.07/0.15 = { by lemma 9 R->L }
% 0.07/0.15 ifeq2(sorti1(j(u)), true, ifeq2(sorti1(j(u)), true, op2(h(j(u)), h(j(u))), h(op1(j(u), j(u)))), h(op1(j(u), j(u))))
% 0.07/0.15 = { by axiom 7 (co1_1) }
% 0.07/0.15 h(op1(j(u), j(u)))
% 0.07/0.15 = { by lemma 9 }
% 0.07/0.15 h(j(u))
% 0.07/0.15 = { by lemma 8 }
% 0.07/0.15 u
% 0.07/0.15 % SZS output end Proof
% 0.07/0.15
% 0.07/0.15 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------