%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ALG019+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 09:06:55 AM UTC 2026
% Result : Theorem 0.22s 0.27s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG019+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.19 % Computer : n007.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 19:16:25 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.27 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
% 0.22/0.27
% 0.22/0.27 % SZS status Theorem
% 0.22/0.27
% 0.22/0.28 % SZS output start Proof
% 0.22/0.28 Axiom 1 (ax4): sorti2(u) = true.
% 0.22/0.28 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.22/0.28 Axiom 3 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.22/0.28 Axiom 4 (ax3_1): ifeq(sorti1(X), true, sorti1(v(X)), true) = true.
% 0.22/0.28 Axiom 5 (co1): ifeq(sorti1(X), true, sorti2(h(X)), true) = true.
% 0.22/0.28 Axiom 6 (co1_3): ifeq(sorti2(X), true, sorti1(j(X)), true) = true.
% 0.22/0.28 Axiom 7 (co1_2): ifeq2(sorti1(X), true, j(h(X)), X) = X.
% 0.22/0.28 Axiom 8 (ax4_1): ifeq2(sorti2(X), true, op2(X, X), u) = u.
% 0.22/0.28 Axiom 9 (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)).
% 0.22/0.28
% 0.22/0.28 Lemma 10: j(h(v(j(u)))) = v(j(u)).
% 0.22/0.28 Proof:
% 0.22/0.28 j(h(v(j(u))))
% 0.22/0.28 = { by axiom 3 (ifeq_axiom) R->L }
% 0.22/0.28 ifeq2(true, true, j(h(v(j(u)))), v(j(u)))
% 0.22/0.28 = { by axiom 4 (ax3_1) R->L }
% 0.22/0.28 ifeq2(ifeq(sorti1(j(u)), true, sorti1(v(j(u))), true), true, j(h(v(j(u)))), v(j(u)))
% 0.22/0.28 = { by axiom 2 (ifeq_axiom) R->L }
% 0.22/0.28 ifeq2(ifeq(ifeq(true, true, sorti1(j(u)), true), true, sorti1(v(j(u))), true), true, j(h(v(j(u)))), v(j(u)))
% 0.22/0.28 = { by axiom 1 (ax4) R->L }
% 0.22/0.28 ifeq2(ifeq(ifeq(sorti2(u), true, sorti1(j(u)), true), true, sorti1(v(j(u))), true), true, j(h(v(j(u)))), v(j(u)))
% 0.22/0.28 = { by axiom 6 (co1_3) }
% 0.22/0.28 ifeq2(ifeq(true, true, sorti1(v(j(u))), true), true, j(h(v(j(u)))), v(j(u)))
% 0.22/0.28 = { by axiom 2 (ifeq_axiom) }
% 0.22/0.28 ifeq2(sorti1(v(j(u))), true, j(h(v(j(u)))), v(j(u)))
% 0.22/0.28 = { by axiom 7 (co1_2) }
% 0.22/0.28 v(j(u))
% 0.22/0.28
% 0.22/0.28 Lemma 11: op2(h(v(j(u))), h(v(j(u)))) = u.
% 0.22/0.28 Proof:
% 0.22/0.28 op2(h(v(j(u))), h(v(j(u))))
% 0.22/0.28 = { by axiom 3 (ifeq_axiom) R->L }
% 0.22/0.28 ifeq2(true, true, op2(h(v(j(u))), h(v(j(u)))), u)
% 0.22/0.28 = { by axiom 5 (co1) R->L }
% 0.22/0.28 ifeq2(ifeq(sorti1(v(j(u))), true, sorti2(h(v(j(u)))), true), true, op2(h(v(j(u))), h(v(j(u)))), u)
% 0.22/0.28 = { by axiom 2 (ifeq_axiom) R->L }
% 0.22/0.28 ifeq2(ifeq(ifeq(true, true, sorti1(v(j(u))), true), true, sorti2(h(v(j(u)))), true), true, op2(h(v(j(u))), h(v(j(u)))), u)
% 0.22/0.28 = { by axiom 6 (co1_3) R->L }
% 0.22/0.28 ifeq2(ifeq(ifeq(ifeq(sorti2(u), true, sorti1(j(u)), true), true, sorti1(v(j(u))), true), true, sorti2(h(v(j(u)))), true), true, op2(h(v(j(u))), h(v(j(u)))), u)
% 0.22/0.28 = { by axiom 1 (ax4) }
% 0.22/0.28 ifeq2(ifeq(ifeq(ifeq(true, true, sorti1(j(u)), true), true, sorti1(v(j(u))), true), true, sorti2(h(v(j(u)))), true), true, op2(h(v(j(u))), h(v(j(u)))), u)
% 0.22/0.28 = { by axiom 2 (ifeq_axiom) }
% 0.22/0.28 ifeq2(ifeq(ifeq(sorti1(j(u)), true, sorti1(v(j(u))), true), true, sorti2(h(v(j(u)))), true), true, op2(h(v(j(u))), h(v(j(u)))), u)
% 0.22/0.28 = { by axiom 4 (ax3_1) }
% 0.22/0.28 ifeq2(ifeq(true, true, sorti2(h(v(j(u)))), true), true, op2(h(v(j(u))), h(v(j(u)))), u)
% 0.22/0.28 = { by axiom 2 (ifeq_axiom) }
% 0.22/0.28 ifeq2(sorti2(h(v(j(u)))), true, op2(h(v(j(u))), h(v(j(u)))), u)
% 0.22/0.28 = { by axiom 8 (ax4_1) }
% 0.22/0.28 u
% 0.22/0.28
% 0.22/0.28 Goal 1 (ax3): tuple(op1(v(X), v(X)), sorti1(X)) = tuple(X, true).
% 0.22/0.28 The goal is true when:
% 0.22/0.28 X = j(u)
% 0.22/0.28
% 0.22/0.28 Proof:
% 0.22/0.28 tuple(op1(v(j(u)), v(j(u))), sorti1(j(u)))
% 0.22/0.28 = { by lemma 10 R->L }
% 0.22/0.28 tuple(op1(j(h(v(j(u)))), v(j(u))), sorti1(j(u)))
% 0.22/0.28 = { by lemma 10 R->L }
% 0.22/0.28 tuple(op1(j(h(v(j(u)))), j(h(v(j(u))))), sorti1(j(u)))
% 0.22/0.28 = { by axiom 3 (ifeq_axiom) R->L }
% 0.22/0.28 tuple(ifeq2(true, true, op1(j(h(v(j(u)))), j(h(v(j(u))))), j(u)), sorti1(j(u)))
% 0.22/0.28 = { by axiom 3 (ifeq_axiom) R->L }
% 0.22/0.28 tuple(ifeq2(true, true, ifeq2(true, true, op1(j(h(v(j(u)))), j(h(v(j(u))))), j(u)), j(op2(h(v(j(u))), h(v(j(u)))))), sorti1(j(u)))
% 0.22/0.28 = { by axiom 5 (co1) R->L }
% 0.22/0.28 tuple(ifeq2(ifeq(sorti1(v(j(u))), true, sorti2(h(v(j(u)))), true), true, ifeq2(true, true, op1(j(h(v(j(u)))), j(h(v(j(u))))), j(u)), j(op2(h(v(j(u))), h(v(j(u)))))), sorti1(j(u)))
% 0.22/0.28 = { by axiom 2 (ifeq_axiom) R->L }
% 0.22/0.28 tuple(ifeq2(ifeq(ifeq(true, true, sorti1(v(j(u))), true), true, sorti2(h(v(j(u)))), true), true, ifeq2(true, true, op1(j(h(v(j(u)))), j(h(v(j(u))))), j(u)), j(op2(h(v(j(u))), h(v(j(u)))))), sorti1(j(u)))
% 0.22/0.28 = { by axiom 6 (co1_3) R->L }
% 0.22/0.28 tuple(ifeq2(ifeq(ifeq(ifeq(sorti2(u), true, sorti1(j(u)), true), true, sorti1(v(j(u))), true), true, sorti2(h(v(j(u)))), true), true, ifeq2(true, true, op1(j(h(v(j(u)))), j(h(v(j(u))))), j(u)), j(op2(h(v(j(u))), h(v(j(u)))))), sorti1(j(u)))
% 0.22/0.28 = { by axiom 1 (ax4) }
% 0.22/0.28 tuple(ifeq2(ifeq(ifeq(ifeq(true, true, sorti1(j(u)), true), true, sorti1(v(j(u))), true), true, sorti2(h(v(j(u)))), true), true, ifeq2(true, true, op1(j(h(v(j(u)))), j(h(v(j(u))))), j(u)), j(op2(h(v(j(u))), h(v(j(u)))))), sorti1(j(u)))
% 0.22/0.28 = { by axiom 2 (ifeq_axiom) }
% 0.22/0.28 tuple(ifeq2(ifeq(ifeq(sorti1(j(u)), true, sorti1(v(j(u))), true), true, sorti2(h(v(j(u)))), true), true, ifeq2(true, true, op1(j(h(v(j(u)))), j(h(v(j(u))))), j(u)), j(op2(h(v(j(u))), h(v(j(u)))))), sorti1(j(u)))
% 0.22/0.28 = { by axiom 4 (ax3_1) }
% 0.22/0.28 tuple(ifeq2(ifeq(true, true, sorti2(h(v(j(u)))), true), true, ifeq2(true, true, op1(j(h(v(j(u)))), j(h(v(j(u))))), j(u)), j(op2(h(v(j(u))), h(v(j(u)))))), sorti1(j(u)))
% 0.22/0.28 = { by axiom 2 (ifeq_axiom) }
% 0.22/0.28 tuple(ifeq2(sorti2(h(v(j(u)))), true, ifeq2(true, true, op1(j(h(v(j(u)))), j(h(v(j(u))))), j(u)), j(op2(h(v(j(u))), h(v(j(u)))))), sorti1(j(u)))
% 0.22/0.28 = { by axiom 5 (co1) R->L }
% 0.22/0.28 tuple(ifeq2(sorti2(h(v(j(u)))), true, ifeq2(ifeq(sorti1(v(j(u))), true, sorti2(h(v(j(u)))), true), true, op1(j(h(v(j(u)))), j(h(v(j(u))))), j(u)), j(op2(h(v(j(u))), h(v(j(u)))))), sorti1(j(u)))
% 0.22/0.28 = { by axiom 2 (ifeq_axiom) R->L }
% 0.22/0.28 tuple(ifeq2(sorti2(h(v(j(u)))), true, ifeq2(ifeq(ifeq(true, true, sorti1(v(j(u))), true), true, sorti2(h(v(j(u)))), true), true, op1(j(h(v(j(u)))), j(h(v(j(u))))), j(u)), j(op2(h(v(j(u))), h(v(j(u)))))), sorti1(j(u)))
% 0.22/0.28 = { by axiom 6 (co1_3) R->L }
% 0.22/0.28 tuple(ifeq2(sorti2(h(v(j(u)))), true, ifeq2(ifeq(ifeq(ifeq(sorti2(u), true, sorti1(j(u)), true), true, sorti1(v(j(u))), true), true, sorti2(h(v(j(u)))), true), true, op1(j(h(v(j(u)))), j(h(v(j(u))))), j(u)), j(op2(h(v(j(u))), h(v(j(u)))))), sorti1(j(u)))
% 0.22/0.28 = { by axiom 1 (ax4) }
% 0.22/0.28 tuple(ifeq2(sorti2(h(v(j(u)))), true, ifeq2(ifeq(ifeq(ifeq(true, true, sorti1(j(u)), true), true, sorti1(v(j(u))), true), true, sorti2(h(v(j(u)))), true), true, op1(j(h(v(j(u)))), j(h(v(j(u))))), j(u)), j(op2(h(v(j(u))), h(v(j(u)))))), sorti1(j(u)))
% 0.22/0.28 = { by axiom 2 (ifeq_axiom) }
% 0.22/0.28 tuple(ifeq2(sorti2(h(v(j(u)))), true, ifeq2(ifeq(ifeq(sorti1(j(u)), true, sorti1(v(j(u))), true), true, sorti2(h(v(j(u)))), true), true, op1(j(h(v(j(u)))), j(h(v(j(u))))), j(u)), j(op2(h(v(j(u))), h(v(j(u)))))), sorti1(j(u)))
% 0.22/0.28 = { by axiom 4 (ax3_1) }
% 0.22/0.28 tuple(ifeq2(sorti2(h(v(j(u)))), true, ifeq2(ifeq(true, true, sorti2(h(v(j(u)))), true), true, op1(j(h(v(j(u)))), j(h(v(j(u))))), j(u)), j(op2(h(v(j(u))), h(v(j(u)))))), sorti1(j(u)))
% 0.22/0.28 = { by axiom 2 (ifeq_axiom) }
% 0.22/0.28 tuple(ifeq2(sorti2(h(v(j(u)))), true, ifeq2(sorti2(h(v(j(u)))), true, op1(j(h(v(j(u)))), j(h(v(j(u))))), j(u)), j(op2(h(v(j(u))), h(v(j(u)))))), sorti1(j(u)))
% 0.22/0.28 = { by lemma 11 R->L }
% 0.22/0.28 tuple(ifeq2(sorti2(h(v(j(u)))), true, ifeq2(sorti2(h(v(j(u)))), true, op1(j(h(v(j(u)))), j(h(v(j(u))))), j(op2(h(v(j(u))), h(v(j(u)))))), j(op2(h(v(j(u))), h(v(j(u)))))), sorti1(j(u)))
% 0.22/0.28 = { by axiom 9 (co1_4) }
% 0.22/0.28 tuple(j(op2(h(v(j(u))), h(v(j(u))))), sorti1(j(u)))
% 0.22/0.28 = { by lemma 11 }
% 0.22/0.28 tuple(j(u), sorti1(j(u)))
% 0.22/0.28 = { by axiom 2 (ifeq_axiom) R->L }
% 0.22/0.28 tuple(j(u), ifeq(true, true, sorti1(j(u)), true))
% 0.22/0.28 = { by axiom 1 (ax4) R->L }
% 0.22/0.28 tuple(j(u), ifeq(sorti2(u), true, sorti1(j(u)), true))
% 0.22/0.28 = { by axiom 6 (co1_3) }
% 0.22/0.28 tuple(j(u), true)
% 0.22/0.28 % SZS output end Proof
% 0.22/0.28
% 0.22/0.28 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------