%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ALG030+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 09:06:56 AM UTC 2026
% Result : Theorem 0.24s 0.35s
% Output : Proof 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG030+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.05 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.22 % Computer : n016.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Mon Sep 28 19:24:18 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.24/0.35 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
% 0.24/0.35
% 0.24/0.35 % SZS status Theorem
% 0.24/0.35
% 0.24/0.35 % SZS output start Proof
% 0.24/0.35 Axiom 1 (ax3): sorti1(u) = true.
% 0.24/0.35 Axiom 2 (ax3_1): sorti1(v) = true.
% 0.24/0.35 Axiom 3 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.24/0.35 Axiom 4 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.24/0.35 Axiom 5 (co1): ifeq(sorti1(X), true, sorti2(h(X)), true) = true.
% 0.24/0.35 Axiom 6 (co1_2): ifeq2(sorti1(X), true, j(h(X)), X) = X.
% 0.24/0.35 Axiom 7 (ax1): ifeq(sorti1(X), true, ifeq(sorti1(Y), true, sorti1(op1(Y, X)), true), true) = true.
% 0.24/0.35 Axiom 8 (ax4): ifeq2(sorti2(X), true, ifeq2(sorti2(Y), true, op2(Y, X), op2(X, Y)), op2(X, Y)) = op2(X, Y).
% 0.24/0.35 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)).
% 0.24/0.35
% 0.24/0.35 Goal 1 (ax3_2): op1(u, v) = op1(v, u).
% 0.24/0.35 Proof:
% 0.24/0.35 op1(u, v)
% 0.24/0.35 = { by axiom 6 (co1_2) R->L }
% 0.24/0.35 ifeq2(sorti1(op1(u, v)), true, j(h(op1(u, v))), op1(u, v))
% 0.24/0.35 = { by axiom 4 (ifeq_axiom) R->L }
% 0.24/0.35 ifeq2(ifeq(true, true, sorti1(op1(u, v)), true), true, j(h(op1(u, v))), op1(u, v))
% 0.24/0.35 = { by axiom 1 (ax3) R->L }
% 0.24/0.35 ifeq2(ifeq(sorti1(u), true, sorti1(op1(u, v)), true), true, j(h(op1(u, v))), op1(u, v))
% 0.24/0.35 = { by axiom 4 (ifeq_axiom) R->L }
% 0.24/0.35 ifeq2(ifeq(true, true, ifeq(sorti1(u), true, sorti1(op1(u, v)), true), true), true, j(h(op1(u, v))), op1(u, v))
% 0.24/0.35 = { by axiom 2 (ax3_1) R->L }
% 0.24/0.35 ifeq2(ifeq(sorti1(v), true, ifeq(sorti1(u), true, sorti1(op1(u, v)), true), true), true, j(h(op1(u, v))), op1(u, v))
% 0.24/0.35 = { by axiom 7 (ax1) }
% 0.24/0.35 ifeq2(true, true, j(h(op1(u, v))), op1(u, v))
% 0.24/0.35 = { by axiom 3 (ifeq_axiom) }
% 0.24/0.35 j(h(op1(u, v)))
% 0.24/0.35 = { by axiom 3 (ifeq_axiom) R->L }
% 0.24/0.35 ifeq2(true, true, j(h(op1(u, v))), op1(v, u))
% 0.24/0.35 = { by axiom 7 (ax1) R->L }
% 0.24/0.35 ifeq2(ifeq(sorti1(u), true, ifeq(sorti1(v), true, sorti1(op1(v, u)), true), true), true, j(h(op1(u, v))), op1(v, u))
% 0.24/0.35 = { by axiom 1 (ax3) }
% 0.24/0.35 ifeq2(ifeq(true, true, ifeq(sorti1(v), true, sorti1(op1(v, u)), true), true), true, j(h(op1(u, v))), op1(v, u))
% 0.24/0.35 = { by axiom 4 (ifeq_axiom) }
% 0.24/0.35 ifeq2(ifeq(sorti1(v), true, sorti1(op1(v, u)), true), true, j(h(op1(u, v))), op1(v, u))
% 0.24/0.35 = { by axiom 2 (ax3_1) }
% 0.24/0.35 ifeq2(ifeq(true, true, sorti1(op1(v, u)), true), true, j(h(op1(u, v))), op1(v, u))
% 0.24/0.35 = { by axiom 4 (ifeq_axiom) }
% 0.24/0.35 ifeq2(sorti1(op1(v, u)), true, j(h(op1(u, v))), op1(v, u))
% 0.24/0.35 = { by axiom 9 (co1_1) R->L }
% 0.24/0.35 ifeq2(sorti1(op1(v, u)), true, j(ifeq2(sorti1(v), true, ifeq2(sorti1(u), true, op2(h(u), h(v)), h(op1(u, v))), h(op1(u, v)))), op1(v, u))
% 0.24/0.35 = { by axiom 2 (ax3_1) }
% 0.24/0.35 ifeq2(sorti1(op1(v, u)), true, j(ifeq2(true, true, ifeq2(sorti1(u), true, op2(h(u), h(v)), h(op1(u, v))), h(op1(u, v)))), op1(v, u))
% 0.24/0.35 = { by axiom 3 (ifeq_axiom) }
% 0.24/0.35 ifeq2(sorti1(op1(v, u)), true, j(ifeq2(sorti1(u), true, op2(h(u), h(v)), h(op1(u, v)))), op1(v, u))
% 0.24/0.35 = { by axiom 1 (ax3) }
% 0.24/0.35 ifeq2(sorti1(op1(v, u)), true, j(ifeq2(true, true, op2(h(u), h(v)), h(op1(u, v)))), op1(v, u))
% 0.24/0.35 = { by axiom 3 (ifeq_axiom) }
% 0.24/0.35 ifeq2(sorti1(op1(v, u)), true, j(op2(h(u), h(v))), op1(v, u))
% 0.24/0.35 = { by axiom 8 (ax4) R->L }
% 0.24/0.35 ifeq2(sorti1(op1(v, u)), true, j(ifeq2(sorti2(h(u)), true, ifeq2(sorti2(h(v)), true, op2(h(v), h(u)), op2(h(u), h(v))), op2(h(u), h(v)))), op1(v, u))
% 0.24/0.35 = { by axiom 3 (ifeq_axiom) R->L }
% 0.24/0.35 ifeq2(sorti1(op1(v, u)), true, j(ifeq2(sorti2(h(u)), true, ifeq2(sorti2(h(v)), true, ifeq2(true, true, op2(h(v), h(u)), h(op1(v, u))), op2(h(u), h(v))), op2(h(u), h(v)))), op1(v, u))
% 0.24/0.35 = { by axiom 2 (ax3_1) R->L }
% 0.24/0.35 ifeq2(sorti1(op1(v, u)), true, j(ifeq2(sorti2(h(u)), true, ifeq2(sorti2(h(v)), true, ifeq2(sorti1(v), true, op2(h(v), h(u)), h(op1(v, u))), op2(h(u), h(v))), op2(h(u), h(v)))), op1(v, u))
% 0.24/0.35 = { by axiom 3 (ifeq_axiom) R->L }
% 0.24/0.35 ifeq2(sorti1(op1(v, u)), true, j(ifeq2(sorti2(h(u)), true, ifeq2(sorti2(h(v)), true, ifeq2(true, true, ifeq2(sorti1(v), true, op2(h(v), h(u)), h(op1(v, u))), h(op1(v, u))), op2(h(u), h(v))), op2(h(u), h(v)))), op1(v, u))
% 0.24/0.35 = { by axiom 1 (ax3) R->L }
% 0.24/0.35 ifeq2(sorti1(op1(v, u)), true, j(ifeq2(sorti2(h(u)), true, ifeq2(sorti2(h(v)), true, ifeq2(sorti1(u), true, ifeq2(sorti1(v), true, op2(h(v), h(u)), h(op1(v, u))), h(op1(v, u))), op2(h(u), h(v))), op2(h(u), h(v)))), op1(v, u))
% 0.24/0.35 = { by axiom 9 (co1_1) }
% 0.24/0.35 ifeq2(sorti1(op1(v, u)), true, j(ifeq2(sorti2(h(u)), true, ifeq2(sorti2(h(v)), true, h(op1(v, u)), op2(h(u), h(v))), op2(h(u), h(v)))), op1(v, u))
% 0.24/0.35 = { by axiom 4 (ifeq_axiom) R->L }
% 0.24/0.35 ifeq2(sorti1(op1(v, u)), true, j(ifeq2(ifeq(true, true, sorti2(h(u)), true), true, ifeq2(sorti2(h(v)), true, h(op1(v, u)), op2(h(u), h(v))), op2(h(u), h(v)))), op1(v, u))
% 0.24/0.35 = { by axiom 1 (ax3) R->L }
% 0.24/0.35 ifeq2(sorti1(op1(v, u)), true, j(ifeq2(ifeq(sorti1(u), true, sorti2(h(u)), true), true, ifeq2(sorti2(h(v)), true, h(op1(v, u)), op2(h(u), h(v))), op2(h(u), h(v)))), op1(v, u))
% 0.24/0.35 = { by axiom 5 (co1) }
% 0.24/0.35 ifeq2(sorti1(op1(v, u)), true, j(ifeq2(true, true, ifeq2(sorti2(h(v)), true, h(op1(v, u)), op2(h(u), h(v))), op2(h(u), h(v)))), op1(v, u))
% 0.24/0.35 = { by axiom 3 (ifeq_axiom) }
% 0.24/0.35 ifeq2(sorti1(op1(v, u)), true, j(ifeq2(sorti2(h(v)), true, h(op1(v, u)), op2(h(u), h(v)))), op1(v, u))
% 0.24/0.35 = { by axiom 4 (ifeq_axiom) R->L }
% 0.24/0.35 ifeq2(sorti1(op1(v, u)), true, j(ifeq2(ifeq(true, true, sorti2(h(v)), true), true, h(op1(v, u)), op2(h(u), h(v)))), op1(v, u))
% 0.24/0.35 = { by axiom 2 (ax3_1) R->L }
% 0.24/0.35 ifeq2(sorti1(op1(v, u)), true, j(ifeq2(ifeq(sorti1(v), true, sorti2(h(v)), true), true, h(op1(v, u)), op2(h(u), h(v)))), op1(v, u))
% 0.24/0.36 = { by axiom 5 (co1) }
% 0.24/0.36 ifeq2(sorti1(op1(v, u)), true, j(ifeq2(true, true, h(op1(v, u)), op2(h(u), h(v)))), op1(v, u))
% 0.24/0.36 = { by axiom 3 (ifeq_axiom) }
% 0.24/0.36 ifeq2(sorti1(op1(v, u)), true, j(h(op1(v, u))), op1(v, u))
% 0.24/0.36 = { by axiom 6 (co1_2) }
% 0.24/0.36 op1(v, u)
% 0.24/0.36 % SZS output end Proof
% 0.24/0.36
% 0.24/0.36 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------