%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ALG040+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 09:06:57 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG040+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n001.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 19:25:48 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.26 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.08/0.26
% 0.08/0.26 % SZS status Theorem
% 0.08/0.26
% 0.08/0.26 % SZS output start Proof
% 0.08/0.26 Axiom 1 (ax3): sorti1(u) = true.
% 0.08/0.26 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.08/0.26 Axiom 3 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.08/0.26 Axiom 4 (ax4_1): ifeq(sorti2(X), true, sorti2(v(X)), true) = true.
% 0.08/0.26 Axiom 5 (co1_3): ifeq(sorti2(X), true, sorti1(j(X)), true) = true.
% 0.08/0.26 Axiom 6 (co1): ifeq(sorti1(X), true, sorti2(h(X)), true) = true.
% 0.08/0.26 Axiom 7 (co1_5): ifeq2(sorti2(X), true, h(j(X)), X) = X.
% 0.08/0.26 Axiom 8 (ax3_1): ifeq2(sorti1(X), true, op1(X, X), u) = u.
% 0.08/0.26 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)).
% 0.08/0.26
% 0.08/0.26 Lemma 10: h(j(v(h(u)))) = v(h(u)).
% 0.08/0.26 Proof:
% 0.08/0.26 h(j(v(h(u))))
% 0.08/0.26 = { by axiom 3 (ifeq_axiom) R->L }
% 0.08/0.26 ifeq2(true, true, h(j(v(h(u)))), v(h(u)))
% 0.08/0.26 = { by axiom 4 (ax4_1) R->L }
% 0.08/0.26 ifeq2(ifeq(sorti2(h(u)), true, sorti2(v(h(u))), true), true, h(j(v(h(u)))), v(h(u)))
% 0.08/0.26 = { by axiom 2 (ifeq_axiom) R->L }
% 0.08/0.26 ifeq2(ifeq(ifeq(true, true, sorti2(h(u)), true), true, sorti2(v(h(u))), true), true, h(j(v(h(u)))), v(h(u)))
% 0.08/0.26 = { by axiom 1 (ax3) R->L }
% 0.08/0.26 ifeq2(ifeq(ifeq(sorti1(u), true, sorti2(h(u)), true), true, sorti2(v(h(u))), true), true, h(j(v(h(u)))), v(h(u)))
% 0.08/0.26 = { by axiom 6 (co1) }
% 0.08/0.26 ifeq2(ifeq(true, true, sorti2(v(h(u))), true), true, h(j(v(h(u)))), v(h(u)))
% 0.08/0.26 = { by axiom 2 (ifeq_axiom) }
% 0.08/0.26 ifeq2(sorti2(v(h(u))), true, h(j(v(h(u)))), v(h(u)))
% 0.08/0.26 = { by axiom 7 (co1_5) }
% 0.08/0.26 v(h(u))
% 0.08/0.26
% 0.08/0.26 Lemma 11: op1(j(v(h(u))), j(v(h(u)))) = u.
% 0.08/0.26 Proof:
% 0.08/0.26 op1(j(v(h(u))), j(v(h(u))))
% 0.08/0.26 = { by axiom 3 (ifeq_axiom) R->L }
% 0.08/0.26 ifeq2(true, true, op1(j(v(h(u))), j(v(h(u)))), u)
% 0.08/0.26 = { by axiom 5 (co1_3) R->L }
% 0.08/0.27 ifeq2(ifeq(sorti2(v(h(u))), true, sorti1(j(v(h(u)))), true), true, op1(j(v(h(u))), j(v(h(u)))), u)
% 0.08/0.27 = { by axiom 2 (ifeq_axiom) R->L }
% 0.08/0.27 ifeq2(ifeq(ifeq(true, true, sorti2(v(h(u))), true), true, sorti1(j(v(h(u)))), true), true, op1(j(v(h(u))), j(v(h(u)))), u)
% 0.08/0.27 = { by axiom 6 (co1) R->L }
% 0.08/0.27 ifeq2(ifeq(ifeq(ifeq(sorti1(u), true, sorti2(h(u)), true), true, sorti2(v(h(u))), true), true, sorti1(j(v(h(u)))), true), true, op1(j(v(h(u))), j(v(h(u)))), u)
% 0.08/0.27 = { by axiom 1 (ax3) }
% 0.08/0.27 ifeq2(ifeq(ifeq(ifeq(true, true, sorti2(h(u)), true), true, sorti2(v(h(u))), true), true, sorti1(j(v(h(u)))), true), true, op1(j(v(h(u))), j(v(h(u)))), u)
% 0.08/0.27 = { by axiom 2 (ifeq_axiom) }
% 0.08/0.27 ifeq2(ifeq(ifeq(sorti2(h(u)), true, sorti2(v(h(u))), true), true, sorti1(j(v(h(u)))), true), true, op1(j(v(h(u))), j(v(h(u)))), u)
% 0.08/0.27 = { by axiom 4 (ax4_1) }
% 0.08/0.27 ifeq2(ifeq(true, true, sorti1(j(v(h(u)))), true), true, op1(j(v(h(u))), j(v(h(u)))), u)
% 0.08/0.27 = { by axiom 2 (ifeq_axiom) }
% 0.08/0.27 ifeq2(sorti1(j(v(h(u)))), true, op1(j(v(h(u))), j(v(h(u)))), u)
% 0.08/0.27 = { by axiom 8 (ax3_1) }
% 0.08/0.27 u
% 0.08/0.27
% 0.08/0.27 Goal 1 (ax4): tuple(op2(v(X), v(X)), sorti2(X)) = tuple(X, true).
% 0.08/0.27 The goal is true when:
% 0.08/0.27 X = h(u)
% 0.08/0.27
% 0.08/0.27 Proof:
% 0.08/0.27 tuple(op2(v(h(u)), v(h(u))), sorti2(h(u)))
% 0.08/0.27 = { by lemma 10 R->L }
% 0.08/0.27 tuple(op2(h(j(v(h(u)))), v(h(u))), sorti2(h(u)))
% 0.08/0.27 = { by lemma 10 R->L }
% 0.08/0.27 tuple(op2(h(j(v(h(u)))), h(j(v(h(u))))), sorti2(h(u)))
% 0.08/0.27 = { by axiom 3 (ifeq_axiom) R->L }
% 0.08/0.27 tuple(ifeq2(true, true, op2(h(j(v(h(u)))), h(j(v(h(u))))), h(u)), sorti2(h(u)))
% 0.08/0.27 = { by axiom 3 (ifeq_axiom) R->L }
% 0.08/0.27 tuple(ifeq2(true, true, ifeq2(true, true, op2(h(j(v(h(u)))), h(j(v(h(u))))), h(u)), h(op1(j(v(h(u))), j(v(h(u)))))), sorti2(h(u)))
% 0.08/0.27 = { by axiom 5 (co1_3) R->L }
% 0.08/0.27 tuple(ifeq2(ifeq(sorti2(v(h(u))), true, sorti1(j(v(h(u)))), true), true, ifeq2(true, true, op2(h(j(v(h(u)))), h(j(v(h(u))))), h(u)), h(op1(j(v(h(u))), j(v(h(u)))))), sorti2(h(u)))
% 0.08/0.27 = { by axiom 2 (ifeq_axiom) R->L }
% 0.08/0.27 tuple(ifeq2(ifeq(ifeq(true, true, sorti2(v(h(u))), true), true, sorti1(j(v(h(u)))), true), true, ifeq2(true, true, op2(h(j(v(h(u)))), h(j(v(h(u))))), h(u)), h(op1(j(v(h(u))), j(v(h(u)))))), sorti2(h(u)))
% 0.08/0.27 = { by axiom 6 (co1) R->L }
% 0.08/0.27 tuple(ifeq2(ifeq(ifeq(ifeq(sorti1(u), true, sorti2(h(u)), true), true, sorti2(v(h(u))), true), true, sorti1(j(v(h(u)))), true), true, ifeq2(true, true, op2(h(j(v(h(u)))), h(j(v(h(u))))), h(u)), h(op1(j(v(h(u))), j(v(h(u)))))), sorti2(h(u)))
% 0.08/0.27 = { by axiom 1 (ax3) }
% 0.08/0.27 tuple(ifeq2(ifeq(ifeq(ifeq(true, true, sorti2(h(u)), true), true, sorti2(v(h(u))), true), true, sorti1(j(v(h(u)))), true), true, ifeq2(true, true, op2(h(j(v(h(u)))), h(j(v(h(u))))), h(u)), h(op1(j(v(h(u))), j(v(h(u)))))), sorti2(h(u)))
% 0.08/0.27 = { by axiom 2 (ifeq_axiom) }
% 0.08/0.27 tuple(ifeq2(ifeq(ifeq(sorti2(h(u)), true, sorti2(v(h(u))), true), true, sorti1(j(v(h(u)))), true), true, ifeq2(true, true, op2(h(j(v(h(u)))), h(j(v(h(u))))), h(u)), h(op1(j(v(h(u))), j(v(h(u)))))), sorti2(h(u)))
% 0.08/0.27 = { by axiom 4 (ax4_1) }
% 0.08/0.27 tuple(ifeq2(ifeq(true, true, sorti1(j(v(h(u)))), true), true, ifeq2(true, true, op2(h(j(v(h(u)))), h(j(v(h(u))))), h(u)), h(op1(j(v(h(u))), j(v(h(u)))))), sorti2(h(u)))
% 0.22/0.27 = { by axiom 2 (ifeq_axiom) }
% 0.22/0.27 tuple(ifeq2(sorti1(j(v(h(u)))), true, ifeq2(true, true, op2(h(j(v(h(u)))), h(j(v(h(u))))), h(u)), h(op1(j(v(h(u))), j(v(h(u)))))), sorti2(h(u)))
% 0.22/0.27 = { by axiom 5 (co1_3) R->L }
% 0.22/0.27 tuple(ifeq2(sorti1(j(v(h(u)))), true, ifeq2(ifeq(sorti2(v(h(u))), true, sorti1(j(v(h(u)))), true), true, op2(h(j(v(h(u)))), h(j(v(h(u))))), h(u)), h(op1(j(v(h(u))), j(v(h(u)))))), sorti2(h(u)))
% 0.22/0.27 = { by axiom 2 (ifeq_axiom) R->L }
% 0.22/0.27 tuple(ifeq2(sorti1(j(v(h(u)))), true, ifeq2(ifeq(ifeq(true, true, sorti2(v(h(u))), true), true, sorti1(j(v(h(u)))), true), true, op2(h(j(v(h(u)))), h(j(v(h(u))))), h(u)), h(op1(j(v(h(u))), j(v(h(u)))))), sorti2(h(u)))
% 0.22/0.27 = { by axiom 6 (co1) R->L }
% 0.22/0.27 tuple(ifeq2(sorti1(j(v(h(u)))), true, ifeq2(ifeq(ifeq(ifeq(sorti1(u), true, sorti2(h(u)), true), true, sorti2(v(h(u))), true), true, sorti1(j(v(h(u)))), true), true, op2(h(j(v(h(u)))), h(j(v(h(u))))), h(u)), h(op1(j(v(h(u))), j(v(h(u)))))), sorti2(h(u)))
% 0.22/0.27 = { by axiom 1 (ax3) }
% 0.22/0.27 tuple(ifeq2(sorti1(j(v(h(u)))), true, ifeq2(ifeq(ifeq(ifeq(true, true, sorti2(h(u)), true), true, sorti2(v(h(u))), true), true, sorti1(j(v(h(u)))), true), true, op2(h(j(v(h(u)))), h(j(v(h(u))))), h(u)), h(op1(j(v(h(u))), j(v(h(u)))))), sorti2(h(u)))
% 0.22/0.27 = { by axiom 2 (ifeq_axiom) }
% 0.22/0.27 tuple(ifeq2(sorti1(j(v(h(u)))), true, ifeq2(ifeq(ifeq(sorti2(h(u)), true, sorti2(v(h(u))), true), true, sorti1(j(v(h(u)))), true), true, op2(h(j(v(h(u)))), h(j(v(h(u))))), h(u)), h(op1(j(v(h(u))), j(v(h(u)))))), sorti2(h(u)))
% 0.22/0.27 = { by axiom 4 (ax4_1) }
% 0.22/0.27 tuple(ifeq2(sorti1(j(v(h(u)))), true, ifeq2(ifeq(true, true, sorti1(j(v(h(u)))), true), true, op2(h(j(v(h(u)))), h(j(v(h(u))))), h(u)), h(op1(j(v(h(u))), j(v(h(u)))))), sorti2(h(u)))
% 0.22/0.27 = { by axiom 2 (ifeq_axiom) }
% 0.22/0.27 tuple(ifeq2(sorti1(j(v(h(u)))), true, ifeq2(sorti1(j(v(h(u)))), true, op2(h(j(v(h(u)))), h(j(v(h(u))))), h(u)), h(op1(j(v(h(u))), j(v(h(u)))))), sorti2(h(u)))
% 0.22/0.27 = { by lemma 11 R->L }
% 0.22/0.27 tuple(ifeq2(sorti1(j(v(h(u)))), true, ifeq2(sorti1(j(v(h(u)))), true, op2(h(j(v(h(u)))), h(j(v(h(u))))), h(op1(j(v(h(u))), j(v(h(u)))))), h(op1(j(v(h(u))), j(v(h(u)))))), sorti2(h(u)))
% 0.22/0.27 = { by axiom 9 (co1_1) }
% 0.22/0.27 tuple(h(op1(j(v(h(u))), j(v(h(u))))), sorti2(h(u)))
% 0.22/0.27 = { by lemma 11 }
% 0.22/0.27 tuple(h(u), sorti2(h(u)))
% 0.22/0.27 = { by axiom 2 (ifeq_axiom) R->L }
% 0.22/0.27 tuple(h(u), ifeq(true, true, sorti2(h(u)), true))
% 0.22/0.27 = { by axiom 1 (ax3) R->L }
% 0.22/0.27 tuple(h(u), ifeq(sorti1(u), true, sorti2(h(u)), true))
% 0.22/0.27 = { by axiom 6 (co1) }
% 0.22/0.27 tuple(h(u), true)
% 0.22/0.27 % SZS output end Proof
% 0.22/0.27
% 0.22/0.27 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------