%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ALG069+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 09:06:59 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG069+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n016.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 19:29:48 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.27 Command-line arguments: --no-flatten-goal
% 0.20/0.27
% 0.20/0.27 % SZS status Theorem
% 0.20/0.27
% 0.20/0.28 % SZS output start Proof
% 0.20/0.28 Axiom 1 (ax4): sorti2(u) = true.
% 0.20/0.28 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.20/0.28 Axiom 3 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.20/0.28 Axiom 4 (ax3_1): ifeq(sorti1(X), true, sorti1(v(X)), true) = true.
% 0.20/0.28 Axiom 5 (co1): ifeq(sorti1(X), true, sorti2(h(X)), true) = true.
% 0.20/0.28 Axiom 6 (co1_3): ifeq(sorti2(X), true, sorti1(j(X)), true) = true.
% 0.20/0.28 Axiom 7 (co1_5): ifeq2(sorti2(X), true, h(j(X)), X) = X.
% 0.20/0.28 Axiom 8 (ax3): ifeq2(sorti1(X), true, op1(v(X), v(X)), X) = X.
% 0.20/0.29 Axiom 9 (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)).
% 0.20/0.29
% 0.20/0.29 Lemma 10: op1(v(j(u)), v(j(u))) = j(u).
% 0.20/0.29 Proof:
% 0.20/0.29 op1(v(j(u)), v(j(u)))
% 0.20/0.29 = { by axiom 3 (ifeq_axiom) R->L }
% 0.20/0.29 ifeq2(true, true, op1(v(j(u)), v(j(u))), j(u))
% 0.20/0.29 = { by axiom 6 (co1_3) R->L }
% 0.20/0.29 ifeq2(ifeq(sorti2(u), true, sorti1(j(u)), true), true, op1(v(j(u)), v(j(u))), j(u))
% 0.20/0.29 = { by axiom 1 (ax4) }
% 0.20/0.29 ifeq2(ifeq(true, true, sorti1(j(u)), true), true, op1(v(j(u)), v(j(u))), j(u))
% 0.20/0.29 = { by axiom 2 (ifeq_axiom) }
% 0.20/0.29 ifeq2(sorti1(j(u)), true, op1(v(j(u)), v(j(u))), j(u))
% 0.20/0.29 = { by axiom 8 (ax3) }
% 0.20/0.29 j(u)
% 0.20/0.29
% 0.20/0.29 Goal 1 (ax4_1): tuple(op2(X, X), sorti2(X)) = tuple(u, true).
% 0.20/0.29 The goal is true when:
% 0.20/0.29 X = h(v(j(u)))
% 0.20/0.29
% 0.20/0.29 Proof:
% 0.20/0.29 tuple(op2(h(v(j(u))), h(v(j(u)))), sorti2(h(v(j(u)))))
% 0.20/0.29 = { by axiom 3 (ifeq_axiom) R->L }
% 0.20/0.29 tuple(ifeq2(true, true, op2(h(v(j(u))), h(v(j(u)))), h(j(u))), sorti2(h(v(j(u)))))
% 0.20/0.29 = { by axiom 3 (ifeq_axiom) R->L }
% 0.20/0.29 tuple(ifeq2(true, true, ifeq2(true, true, op2(h(v(j(u))), h(v(j(u)))), h(j(u))), h(op1(v(j(u)), v(j(u))))), sorti2(h(v(j(u)))))
% 0.20/0.29 = { by axiom 4 (ax3_1) R->L }
% 0.20/0.29 tuple(ifeq2(ifeq(sorti1(j(u)), true, sorti1(v(j(u))), true), true, ifeq2(true, true, op2(h(v(j(u))), h(v(j(u)))), h(j(u))), h(op1(v(j(u)), v(j(u))))), sorti2(h(v(j(u)))))
% 0.20/0.29 = { by axiom 2 (ifeq_axiom) R->L }
% 0.20/0.29 tuple(ifeq2(ifeq(ifeq(true, true, sorti1(j(u)), true), true, sorti1(v(j(u))), true), true, ifeq2(true, true, op2(h(v(j(u))), h(v(j(u)))), h(j(u))), h(op1(v(j(u)), v(j(u))))), sorti2(h(v(j(u)))))
% 0.20/0.29 = { by axiom 1 (ax4) R->L }
% 0.20/0.29 tuple(ifeq2(ifeq(ifeq(sorti2(u), true, sorti1(j(u)), true), true, sorti1(v(j(u))), true), true, ifeq2(true, true, op2(h(v(j(u))), h(v(j(u)))), h(j(u))), h(op1(v(j(u)), v(j(u))))), sorti2(h(v(j(u)))))
% 0.20/0.29 = { by axiom 6 (co1_3) }
% 0.20/0.29 tuple(ifeq2(ifeq(true, true, sorti1(v(j(u))), true), true, ifeq2(true, true, op2(h(v(j(u))), h(v(j(u)))), h(j(u))), h(op1(v(j(u)), v(j(u))))), sorti2(h(v(j(u)))))
% 0.20/0.29 = { by axiom 2 (ifeq_axiom) }
% 0.20/0.29 tuple(ifeq2(sorti1(v(j(u))), true, ifeq2(true, true, op2(h(v(j(u))), h(v(j(u)))), h(j(u))), h(op1(v(j(u)), v(j(u))))), sorti2(h(v(j(u)))))
% 0.20/0.29 = { by axiom 4 (ax3_1) R->L }
% 0.20/0.29 tuple(ifeq2(sorti1(v(j(u))), true, ifeq2(ifeq(sorti1(j(u)), true, sorti1(v(j(u))), true), true, op2(h(v(j(u))), h(v(j(u)))), h(j(u))), h(op1(v(j(u)), v(j(u))))), sorti2(h(v(j(u)))))
% 0.20/0.29 = { by axiom 2 (ifeq_axiom) R->L }
% 0.20/0.29 tuple(ifeq2(sorti1(v(j(u))), true, ifeq2(ifeq(ifeq(true, true, sorti1(j(u)), true), true, sorti1(v(j(u))), true), true, op2(h(v(j(u))), h(v(j(u)))), h(j(u))), h(op1(v(j(u)), v(j(u))))), sorti2(h(v(j(u)))))
% 0.20/0.29 = { by axiom 1 (ax4) R->L }
% 0.20/0.29 tuple(ifeq2(sorti1(v(j(u))), true, ifeq2(ifeq(ifeq(sorti2(u), true, sorti1(j(u)), true), true, sorti1(v(j(u))), true), true, op2(h(v(j(u))), h(v(j(u)))), h(j(u))), h(op1(v(j(u)), v(j(u))))), sorti2(h(v(j(u)))))
% 0.20/0.29 = { by axiom 6 (co1_3) }
% 0.20/0.29 tuple(ifeq2(sorti1(v(j(u))), true, ifeq2(ifeq(true, true, sorti1(v(j(u))), true), true, op2(h(v(j(u))), h(v(j(u)))), h(j(u))), h(op1(v(j(u)), v(j(u))))), sorti2(h(v(j(u)))))
% 0.20/0.29 = { by axiom 2 (ifeq_axiom) }
% 0.20/0.29 tuple(ifeq2(sorti1(v(j(u))), true, ifeq2(sorti1(v(j(u))), true, op2(h(v(j(u))), h(v(j(u)))), h(j(u))), h(op1(v(j(u)), v(j(u))))), sorti2(h(v(j(u)))))
% 0.20/0.29 = { by lemma 10 R->L }
% 0.20/0.29 tuple(ifeq2(sorti1(v(j(u))), true, ifeq2(sorti1(v(j(u))), true, op2(h(v(j(u))), h(v(j(u)))), h(op1(v(j(u)), v(j(u))))), h(op1(v(j(u)), v(j(u))))), sorti2(h(v(j(u)))))
% 0.20/0.29 = { by axiom 9 (co1_1) }
% 0.20/0.29 tuple(h(op1(v(j(u)), v(j(u)))), sorti2(h(v(j(u)))))
% 0.20/0.29 = { by lemma 10 }
% 0.20/0.29 tuple(h(j(u)), sorti2(h(v(j(u)))))
% 0.20/0.29 = { by axiom 3 (ifeq_axiom) R->L }
% 0.20/0.29 tuple(ifeq2(true, true, h(j(u)), u), sorti2(h(v(j(u)))))
% 0.20/0.29 = { by axiom 1 (ax4) R->L }
% 0.20/0.29 tuple(ifeq2(sorti2(u), true, h(j(u)), u), sorti2(h(v(j(u)))))
% 0.20/0.29 = { by axiom 7 (co1_5) }
% 0.20/0.29 tuple(u, sorti2(h(v(j(u)))))
% 0.20/0.29 = { by axiom 2 (ifeq_axiom) R->L }
% 0.20/0.29 tuple(u, ifeq(true, true, sorti2(h(v(j(u)))), true))
% 0.20/0.29 = { by axiom 4 (ax3_1) R->L }
% 0.20/0.29 tuple(u, ifeq(ifeq(sorti1(j(u)), true, sorti1(v(j(u))), true), true, sorti2(h(v(j(u)))), true))
% 0.20/0.29 = { by axiom 2 (ifeq_axiom) R->L }
% 0.20/0.29 tuple(u, ifeq(ifeq(ifeq(true, true, sorti1(j(u)), true), true, sorti1(v(j(u))), true), true, sorti2(h(v(j(u)))), true))
% 0.20/0.29 = { by axiom 1 (ax4) R->L }
% 0.20/0.29 tuple(u, ifeq(ifeq(ifeq(sorti2(u), true, sorti1(j(u)), true), true, sorti1(v(j(u))), true), true, sorti2(h(v(j(u)))), true))
% 0.20/0.29 = { by axiom 6 (co1_3) }
% 0.20/0.29 tuple(u, ifeq(ifeq(true, true, sorti1(v(j(u))), true), true, sorti2(h(v(j(u)))), true))
% 0.20/0.29 = { by axiom 2 (ifeq_axiom) }
% 0.20/0.29 tuple(u, ifeq(sorti1(v(j(u))), true, sorti2(h(v(j(u)))), true))
% 0.20/0.29 = { by axiom 5 (co1) }
% 0.20/0.29 tuple(u, true)
% 0.20/0.29 % SZS output end Proof
% 0.20/0.29
% 0.20/0.29 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------