%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ALG073+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/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 09:06:59 AM UTC 2026
% Result : Theorem 0.09s 0.24s
% Output : Proof 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG073+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.15 % Computer : n001.cluster.edu
% 0.09/0.15 % Model : x86_64 x86_64
% 0.09/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.15 % Memory : 8046.5625MB
% 0.09/0.15 % OS : Linux 6.8.0-71-generic
% 0.09/0.15 % CPULimit : 300
% 0.09/0.15 % WCLimit : 300
% 0.09/0.16 % DateTime : Mon Sep 28 19:30:33 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.24 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-regeneralise
% 0.09/0.24
% 0.09/0.24 % SZS status Theorem
% 0.09/0.24
% 0.09/0.25 % SZS output start Proof
% 0.09/0.25 Axiom 1 (ax3_2): sorti1(u) = true.
% 0.09/0.25 Axiom 2 (ax3_3): sorti1(v) = true.
% 0.09/0.25 Axiom 3 (ax3): op1(u, u) = v.
% 0.09/0.25 Axiom 4 (ax3_1): op1(v, v) = u.
% 0.09/0.25 Axiom 5 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.09/0.25 Axiom 6 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.09/0.25 Axiom 7 (ifeq_axiom): ifeq3(X, X, Y, Z) = Y.
% 0.09/0.25 Axiom 8 (co1): ifeq(sorti1(X), true, sorti2(h(X)), true) = true.
% 0.09/0.25 Axiom 9 (co1_2): ifeq2(sorti1(X), true, j(h(X)), X) = X.
% 0.09/0.25 Axiom 10 (ax1): ifeq(sorti1(X), true, ifeq(sorti1(Y), true, sorti1(op1(Y, X)), true), true) = true.
% 0.09/0.25 Axiom 11 (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)).
% 0.09/0.25 Axiom 12 (ax4): ifeq2(sorti2(X), true, ifeq2(sorti2(Y), true, ifeq3(op2(Y, Y), X, ifeq3(op2(X, X), Y, op2(Y, X), Y), Y), Y), Y) = Y.
% 0.09/0.25
% 0.09/0.25 Goal 1 (ax3_4): op1(u, v) = u.
% 0.09/0.25 Proof:
% 0.09/0.25 op1(u, v)
% 0.09/0.25 = { by axiom 9 (co1_2) R->L }
% 0.09/0.25 ifeq2(sorti1(op1(u, v)), true, j(h(op1(u, v))), op1(u, v))
% 0.09/0.25 = { by axiom 7 (ifeq_axiom) R->L }
% 0.09/0.25 ifeq2(sorti1(op1(u, v)), true, j(ifeq3(h(u), h(u), h(op1(u, v)), h(u))), op1(u, v))
% 0.09/0.26 = { by axiom 4 (ax3_1) R->L }
% 0.09/0.26 ifeq2(sorti1(op1(u, v)), true, j(ifeq3(h(op1(v, v)), h(u), h(op1(u, v)), h(u))), op1(u, v))
% 0.09/0.26 = { by axiom 11 (co1_1) R->L }
% 0.09/0.26 ifeq2(sorti1(op1(u, v)), true, j(ifeq3(ifeq2(sorti1(v), true, ifeq2(sorti1(v), true, op2(h(v), h(v)), h(op1(v, v))), h(op1(v, v))), h(u), h(op1(u, v)), h(u))), op1(u, v))
% 0.09/0.26 = { by axiom 4 (ax3_1) }
% 0.09/0.26 ifeq2(sorti1(op1(u, v)), true, j(ifeq3(ifeq2(sorti1(v), true, ifeq2(sorti1(v), true, op2(h(v), h(v)), h(u)), h(op1(v, v))), h(u), h(op1(u, v)), h(u))), op1(u, v))
% 0.09/0.26 = { by axiom 2 (ax3_3) }
% 0.09/0.26 ifeq2(sorti1(op1(u, v)), true, j(ifeq3(ifeq2(sorti1(v), true, ifeq2(true, true, op2(h(v), h(v)), h(u)), h(op1(v, v))), h(u), h(op1(u, v)), h(u))), op1(u, v))
% 0.09/0.26 = { by axiom 2 (ax3_3) }
% 0.09/0.26 ifeq2(sorti1(op1(u, v)), true, j(ifeq3(ifeq2(true, true, ifeq2(true, true, op2(h(v), h(v)), h(u)), h(op1(v, v))), h(u), h(op1(u, v)), h(u))), op1(u, v))
% 0.09/0.26 = { by axiom 5 (ifeq_axiom) }
% 0.09/0.26 ifeq2(sorti1(op1(u, v)), true, j(ifeq3(ifeq2(true, true, op2(h(v), h(v)), h(u)), h(u), h(op1(u, v)), h(u))), op1(u, v))
% 0.09/0.26 = { by axiom 5 (ifeq_axiom) }
% 0.09/0.26 ifeq2(sorti1(op1(u, v)), true, j(ifeq3(op2(h(v), h(v)), h(u), h(op1(u, v)), h(u))), op1(u, v))
% 0.09/0.26 = { by axiom 7 (ifeq_axiom) R->L }
% 0.09/0.26 ifeq2(sorti1(op1(u, v)), true, j(ifeq3(h(v), h(v), ifeq3(op2(h(v), h(v)), h(u), h(op1(u, v)), h(u)), h(u))), op1(u, v))
% 0.09/0.26 = { by axiom 3 (ax3) R->L }
% 0.09/0.26 ifeq2(sorti1(op1(u, v)), true, j(ifeq3(h(op1(u, u)), h(v), ifeq3(op2(h(v), h(v)), h(u), h(op1(u, v)), h(u)), h(u))), op1(u, v))
% 0.09/0.26 = { by axiom 11 (co1_1) R->L }
% 0.09/0.26 ifeq2(sorti1(op1(u, v)), true, j(ifeq3(ifeq2(sorti1(u), true, ifeq2(sorti1(u), true, op2(h(u), h(u)), h(op1(u, u))), h(op1(u, u))), h(v), ifeq3(op2(h(v), h(v)), h(u), h(op1(u, v)), h(u)), h(u))), op1(u, v))
% 0.09/0.26 = { by axiom 3 (ax3) }
% 0.09/0.26 ifeq2(sorti1(op1(u, v)), true, j(ifeq3(ifeq2(sorti1(u), true, ifeq2(sorti1(u), true, op2(h(u), h(u)), h(v)), h(op1(u, u))), h(v), ifeq3(op2(h(v), h(v)), h(u), h(op1(u, v)), h(u)), h(u))), op1(u, v))
% 0.09/0.26 = { by axiom 1 (ax3_2) }
% 0.09/0.26 ifeq2(sorti1(op1(u, v)), true, j(ifeq3(ifeq2(sorti1(u), true, ifeq2(true, true, op2(h(u), h(u)), h(v)), h(op1(u, u))), h(v), ifeq3(op2(h(v), h(v)), h(u), h(op1(u, v)), h(u)), h(u))), op1(u, v))
% 0.09/0.26 = { by axiom 1 (ax3_2) }
% 0.09/0.26 ifeq2(sorti1(op1(u, v)), true, j(ifeq3(ifeq2(true, true, ifeq2(true, true, op2(h(u), h(u)), h(v)), h(op1(u, u))), h(v), ifeq3(op2(h(v), h(v)), h(u), h(op1(u, v)), h(u)), h(u))), op1(u, v))
% 0.09/0.26 = { by axiom 5 (ifeq_axiom) }
% 0.09/0.26 ifeq2(sorti1(op1(u, v)), true, j(ifeq3(ifeq2(true, true, op2(h(u), h(u)), h(v)), h(v), ifeq3(op2(h(v), h(v)), h(u), h(op1(u, v)), h(u)), h(u))), op1(u, v))
% 0.09/0.26 = { by axiom 5 (ifeq_axiom) }
% 0.09/0.26 ifeq2(sorti1(op1(u, v)), true, j(ifeq3(op2(h(u), h(u)), h(v), ifeq3(op2(h(v), h(v)), h(u), h(op1(u, v)), h(u)), h(u))), op1(u, v))
% 0.09/0.26 = { by axiom 5 (ifeq_axiom) R->L }
% 0.09/0.26 ifeq2(sorti1(op1(u, v)), true, j(ifeq2(true, true, ifeq3(op2(h(u), h(u)), h(v), ifeq3(op2(h(v), h(v)), h(u), h(op1(u, v)), h(u)), h(u)), h(u))), op1(u, v))
% 0.09/0.26 = { by axiom 8 (co1) R->L }
% 0.09/0.26 ifeq2(sorti1(op1(u, v)), true, j(ifeq2(ifeq(sorti1(u), true, sorti2(h(u)), true), true, ifeq3(op2(h(u), h(u)), h(v), ifeq3(op2(h(v), h(v)), h(u), h(op1(u, v)), h(u)), h(u)), h(u))), op1(u, v))
% 0.09/0.26 = { by axiom 1 (ax3_2) }
% 0.09/0.26 ifeq2(sorti1(op1(u, v)), true, j(ifeq2(ifeq(true, true, sorti2(h(u)), true), true, ifeq3(op2(h(u), h(u)), h(v), ifeq3(op2(h(v), h(v)), h(u), h(op1(u, v)), h(u)), h(u)), h(u))), op1(u, v))
% 0.09/0.26 = { by axiom 6 (ifeq_axiom) }
% 0.09/0.26 ifeq2(sorti1(op1(u, v)), true, j(ifeq2(sorti2(h(u)), true, ifeq3(op2(h(u), h(u)), h(v), ifeq3(op2(h(v), h(v)), h(u), h(op1(u, v)), h(u)), h(u)), h(u))), op1(u, v))
% 0.09/0.26 = { by axiom 5 (ifeq_axiom) R->L }
% 0.09/0.26 ifeq2(sorti1(op1(u, v)), true, j(ifeq2(true, true, ifeq2(sorti2(h(u)), true, ifeq3(op2(h(u), h(u)), h(v), ifeq3(op2(h(v), h(v)), h(u), h(op1(u, v)), h(u)), h(u)), h(u)), h(u))), op1(u, v))
% 0.09/0.26 = { by axiom 8 (co1) R->L }
% 0.09/0.26 ifeq2(sorti1(op1(u, v)), true, j(ifeq2(ifeq(sorti1(v), true, sorti2(h(v)), true), true, ifeq2(sorti2(h(u)), true, ifeq3(op2(h(u), h(u)), h(v), ifeq3(op2(h(v), h(v)), h(u), h(op1(u, v)), h(u)), h(u)), h(u)), h(u))), op1(u, v))
% 0.09/0.26 = { by axiom 2 (ax3_3) }
% 0.09/0.26 ifeq2(sorti1(op1(u, v)), true, j(ifeq2(ifeq(true, true, sorti2(h(v)), true), true, ifeq2(sorti2(h(u)), true, ifeq3(op2(h(u), h(u)), h(v), ifeq3(op2(h(v), h(v)), h(u), h(op1(u, v)), h(u)), h(u)), h(u)), h(u))), op1(u, v))
% 0.09/0.26 = { by axiom 6 (ifeq_axiom) }
% 0.09/0.26 ifeq2(sorti1(op1(u, v)), true, j(ifeq2(sorti2(h(v)), true, ifeq2(sorti2(h(u)), true, ifeq3(op2(h(u), h(u)), h(v), ifeq3(op2(h(v), h(v)), h(u), h(op1(u, v)), h(u)), h(u)), h(u)), h(u))), op1(u, v))
% 0.09/0.26 = { by axiom 11 (co1_1) R->L }
% 0.09/0.26 ifeq2(sorti1(op1(u, v)), true, j(ifeq2(sorti2(h(v)), true, ifeq2(sorti2(h(u)), true, ifeq3(op2(h(u), h(u)), h(v), ifeq3(op2(h(v), h(v)), h(u), ifeq2(sorti1(v), true, ifeq2(sorti1(u), true, op2(h(u), h(v)), h(op1(u, v))), h(op1(u, v))), h(u)), h(u)), h(u)), h(u))), op1(u, v))
% 0.09/0.26 = { by axiom 2 (ax3_3) }
% 0.09/0.26 ifeq2(sorti1(op1(u, v)), true, j(ifeq2(sorti2(h(v)), true, ifeq2(sorti2(h(u)), true, ifeq3(op2(h(u), h(u)), h(v), ifeq3(op2(h(v), h(v)), h(u), ifeq2(true, true, ifeq2(sorti1(u), true, op2(h(u), h(v)), h(op1(u, v))), h(op1(u, v))), h(u)), h(u)), h(u)), h(u))), op1(u, v))
% 0.09/0.27 = { by axiom 5 (ifeq_axiom) }
% 0.09/0.27 ifeq2(sorti1(op1(u, v)), true, j(ifeq2(sorti2(h(v)), true, ifeq2(sorti2(h(u)), true, ifeq3(op2(h(u), h(u)), h(v), ifeq3(op2(h(v), h(v)), h(u), ifeq2(sorti1(u), true, op2(h(u), h(v)), h(op1(u, v))), h(u)), h(u)), h(u)), h(u))), op1(u, v))
% 0.09/0.27 = { by axiom 1 (ax3_2) }
% 0.09/0.27 ifeq2(sorti1(op1(u, v)), true, j(ifeq2(sorti2(h(v)), true, ifeq2(sorti2(h(u)), true, ifeq3(op2(h(u), h(u)), h(v), ifeq3(op2(h(v), h(v)), h(u), ifeq2(true, true, op2(h(u), h(v)), h(op1(u, v))), h(u)), h(u)), h(u)), h(u))), op1(u, v))
% 0.09/0.27 = { by axiom 5 (ifeq_axiom) }
% 0.09/0.27 ifeq2(sorti1(op1(u, v)), true, j(ifeq2(sorti2(h(v)), true, ifeq2(sorti2(h(u)), true, ifeq3(op2(h(u), h(u)), h(v), ifeq3(op2(h(v), h(v)), h(u), op2(h(u), h(v)), h(u)), h(u)), h(u)), h(u))), op1(u, v))
% 0.09/0.27 = { by axiom 12 (ax4) }
% 0.09/0.27 ifeq2(sorti1(op1(u, v)), true, j(h(u)), op1(u, v))
% 0.09/0.27 = { by axiom 6 (ifeq_axiom) R->L }
% 0.09/0.27 ifeq2(ifeq(true, true, sorti1(op1(u, v)), true), true, j(h(u)), op1(u, v))
% 0.09/0.27 = { by axiom 1 (ax3_2) R->L }
% 0.09/0.27 ifeq2(ifeq(sorti1(u), true, sorti1(op1(u, v)), true), true, j(h(u)), op1(u, v))
% 0.09/0.27 = { by axiom 6 (ifeq_axiom) R->L }
% 0.09/0.27 ifeq2(ifeq(true, true, ifeq(sorti1(u), true, sorti1(op1(u, v)), true), true), true, j(h(u)), op1(u, v))
% 0.09/0.27 = { by axiom 2 (ax3_3) R->L }
% 0.09/0.27 ifeq2(ifeq(sorti1(v), true, ifeq(sorti1(u), true, sorti1(op1(u, v)), true), true), true, j(h(u)), op1(u, v))
% 0.09/0.27 = { by axiom 10 (ax1) }
% 0.09/0.27 ifeq2(true, true, j(h(u)), op1(u, v))
% 0.09/0.27 = { by axiom 5 (ifeq_axiom) }
% 0.09/0.27 j(h(u))
% 0.09/0.27 = { by axiom 5 (ifeq_axiom) R->L }
% 0.09/0.27 ifeq2(true, true, j(h(u)), u)
% 0.09/0.27 = { by axiom 1 (ax3_2) R->L }
% 0.09/0.27 ifeq2(sorti1(u), true, j(h(u)), u)
% 0.09/0.27 = { by axiom 9 (co1_2) }
% 0.09/0.27 u
% 0.09/0.27 % SZS output end Proof
% 0.09/0.27
% 0.09/0.27 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------