%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ALG179+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 09:07:07 AM UTC 2026
% Result : Theorem 0.04s 0.24s
% Output : Proof 0.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG179+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.16 % Computer : n020.cluster.edu
% 0.04/0.16 % Model : x86_64 x86_64
% 0.04/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.16 % Memory : 8046.5625MB
% 0.04/0.16 % OS : Linux 6.8.0-71-generic
% 0.04/0.16 % CPULimit : 300
% 0.04/0.16 % WCLimit : 300
% 0.04/0.16 % DateTime : Mon Sep 28 19:39:34 UTC 2026
% 0.04/0.17 % CPUTime :
% 0.04/0.17 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.24 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 0.04/0.24
% 0.04/0.24 % SZS status Theorem
% 0.04/0.24
% 0.04/0.25 % SZS output start Proof
% 0.04/0.25 Axiom 1 (ax4_1): sorti2(v) = true.
% 0.04/0.25 Axiom 2 (ax4): sorti2(u) = true.
% 0.04/0.25 Axiom 3 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.04/0.25 Axiom 4 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.04/0.25 Axiom 5 (co1_5): ifeq2(sorti2(X), true, h(j(X)), X) = X.
% 0.04/0.25 Axiom 6 (co1_3): ifeq(sorti2(X), true, sorti1(j(X)), true) = true.
% 0.04/0.25 Axiom 7 (ax2): ifeq(sorti2(X), true, ifeq(sorti2(Y), true, sorti2(op2(Y, X)), true), true) = true.
% 0.04/0.25 Axiom 8 (ax3): ifeq2(sorti1(X), true, ifeq2(sorti1(Y), true, op1(op1(Y, X), X), Y), Y) = Y.
% 0.04/0.25 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)).
% 0.04/0.25 Axiom 10 (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)).
% 0.04/0.25
% 0.04/0.25 Lemma 11: op1(j(op2(u, v)), j(v)) = j(u).
% 0.04/0.25 Proof:
% 0.04/0.25 op1(j(op2(u, v)), j(v))
% 0.04/0.25 = { by axiom 3 (ifeq_axiom) R->L }
% 0.04/0.25 ifeq2(true, true, op1(j(op2(u, v)), j(v)), j(u))
% 0.04/0.25 = { by axiom 6 (co1_3) R->L }
% 0.04/0.25 ifeq2(ifeq(sorti2(u), true, sorti1(j(u)), true), true, op1(j(op2(u, v)), j(v)), j(u))
% 0.04/0.25 = { by axiom 2 (ax4) }
% 0.04/0.25 ifeq2(ifeq(true, true, sorti1(j(u)), true), true, op1(j(op2(u, v)), j(v)), j(u))
% 0.04/0.25 = { by axiom 4 (ifeq_axiom) }
% 0.04/0.25 ifeq2(sorti1(j(u)), true, op1(j(op2(u, v)), j(v)), j(u))
% 0.04/0.25 = { by axiom 3 (ifeq_axiom) R->L }
% 0.04/0.25 ifeq2(true, true, ifeq2(sorti1(j(u)), true, op1(j(op2(u, v)), j(v)), j(u)), j(u))
% 0.04/0.25 = { by axiom 6 (co1_3) R->L }
% 0.04/0.25 ifeq2(ifeq(sorti2(v), true, sorti1(j(v)), true), true, ifeq2(sorti1(j(u)), true, op1(j(op2(u, v)), j(v)), j(u)), j(u))
% 0.04/0.25 = { by axiom 1 (ax4_1) }
% 0.04/0.25 ifeq2(ifeq(true, true, sorti1(j(v)), true), true, ifeq2(sorti1(j(u)), true, op1(j(op2(u, v)), j(v)), j(u)), j(u))
% 0.04/0.25 = { by axiom 4 (ifeq_axiom) }
% 0.04/0.25 ifeq2(sorti1(j(v)), true, ifeq2(sorti1(j(u)), true, op1(j(op2(u, v)), j(v)), j(u)), j(u))
% 0.04/0.25 = { by axiom 9 (co1_4) R->L }
% 0.04/0.25 ifeq2(sorti1(j(v)), true, ifeq2(sorti1(j(u)), true, op1(ifeq2(sorti2(v), true, ifeq2(sorti2(u), true, op1(j(u), j(v)), j(op2(u, v))), j(op2(u, v))), j(v)), j(u)), j(u))
% 0.04/0.25 = { by axiom 1 (ax4_1) }
% 0.04/0.25 ifeq2(sorti1(j(v)), true, ifeq2(sorti1(j(u)), true, op1(ifeq2(true, true, ifeq2(sorti2(u), true, op1(j(u), j(v)), j(op2(u, v))), j(op2(u, v))), j(v)), j(u)), j(u))
% 0.04/0.25 = { by axiom 3 (ifeq_axiom) }
% 0.04/0.25 ifeq2(sorti1(j(v)), true, ifeq2(sorti1(j(u)), true, op1(ifeq2(sorti2(u), true, op1(j(u), j(v)), j(op2(u, v))), j(v)), j(u)), j(u))
% 0.04/0.25 = { by axiom 2 (ax4) }
% 0.04/0.25 ifeq2(sorti1(j(v)), true, ifeq2(sorti1(j(u)), true, op1(ifeq2(true, true, op1(j(u), j(v)), j(op2(u, v))), j(v)), j(u)), j(u))
% 0.04/0.25 = { by axiom 3 (ifeq_axiom) }
% 0.04/0.25 ifeq2(sorti1(j(v)), true, ifeq2(sorti1(j(u)), true, op1(op1(j(u), j(v)), j(v)), j(u)), j(u))
% 0.04/0.25 = { by axiom 8 (ax3) }
% 0.04/0.25 j(u)
% 0.04/0.25
% 0.04/0.25 Goal 1 (ax4_2): op2(op2(u, v), v) = u.
% 0.04/0.25 Proof:
% 0.04/0.25 op2(op2(u, v), v)
% 0.04/0.25 = { by axiom 5 (co1_5) R->L }
% 0.04/0.25 op2(op2(u, v), ifeq2(sorti2(v), true, h(j(v)), v))
% 0.04/0.25 = { by axiom 1 (ax4_1) }
% 0.04/0.25 op2(op2(u, v), ifeq2(true, true, h(j(v)), v))
% 0.04/0.25 = { by axiom 3 (ifeq_axiom) }
% 0.04/0.25 op2(op2(u, v), h(j(v)))
% 0.04/0.25 = { by axiom 5 (co1_5) R->L }
% 0.04/0.25 op2(ifeq2(sorti2(op2(u, v)), true, h(j(op2(u, v))), op2(u, v)), h(j(v)))
% 0.04/0.25 = { by axiom 4 (ifeq_axiom) R->L }
% 0.04/0.25 op2(ifeq2(ifeq(true, true, sorti2(op2(u, v)), true), true, h(j(op2(u, v))), op2(u, v)), h(j(v)))
% 0.04/0.25 = { by axiom 2 (ax4) R->L }
% 0.04/0.25 op2(ifeq2(ifeq(sorti2(u), true, sorti2(op2(u, v)), true), true, h(j(op2(u, v))), op2(u, v)), h(j(v)))
% 0.04/0.25 = { by axiom 4 (ifeq_axiom) R->L }
% 0.04/0.25 op2(ifeq2(ifeq(true, true, ifeq(sorti2(u), true, sorti2(op2(u, v)), true), true), true, h(j(op2(u, v))), op2(u, v)), h(j(v)))
% 0.04/0.25 = { by axiom 1 (ax4_1) R->L }
% 0.04/0.25 op2(ifeq2(ifeq(sorti2(v), true, ifeq(sorti2(u), true, sorti2(op2(u, v)), true), true), true, h(j(op2(u, v))), op2(u, v)), h(j(v)))
% 0.04/0.25 = { by axiom 7 (ax2) }
% 0.04/0.25 op2(ifeq2(true, true, h(j(op2(u, v))), op2(u, v)), h(j(v)))
% 0.04/0.25 = { by axiom 3 (ifeq_axiom) }
% 0.04/0.25 op2(h(j(op2(u, v))), h(j(v)))
% 0.04/0.25 = { by axiom 3 (ifeq_axiom) R->L }
% 0.04/0.25 ifeq2(true, true, op2(h(j(op2(u, v))), h(j(v))), h(j(u)))
% 0.04/0.25 = { by axiom 6 (co1_3) R->L }
% 0.04/0.25 ifeq2(ifeq(sorti2(op2(u, v)), true, sorti1(j(op2(u, v))), true), true, op2(h(j(op2(u, v))), h(j(v))), h(j(u)))
% 0.04/0.25 = { by axiom 4 (ifeq_axiom) R->L }
% 0.04/0.25 ifeq2(ifeq(ifeq(true, true, sorti2(op2(u, v)), true), true, sorti1(j(op2(u, v))), true), true, op2(h(j(op2(u, v))), h(j(v))), h(j(u)))
% 0.04/0.25 = { by axiom 2 (ax4) R->L }
% 0.04/0.25 ifeq2(ifeq(ifeq(sorti2(u), true, sorti2(op2(u, v)), true), true, sorti1(j(op2(u, v))), true), true, op2(h(j(op2(u, v))), h(j(v))), h(j(u)))
% 0.04/0.25 = { by axiom 4 (ifeq_axiom) R->L }
% 0.04/0.25 ifeq2(ifeq(ifeq(true, true, ifeq(sorti2(u), true, sorti2(op2(u, v)), true), true), true, sorti1(j(op2(u, v))), true), true, op2(h(j(op2(u, v))), h(j(v))), h(j(u)))
% 0.04/0.25 = { by axiom 1 (ax4_1) R->L }
% 0.04/0.25 ifeq2(ifeq(ifeq(sorti2(v), true, ifeq(sorti2(u), true, sorti2(op2(u, v)), true), true), true, sorti1(j(op2(u, v))), true), true, op2(h(j(op2(u, v))), h(j(v))), h(j(u)))
% 0.04/0.25 = { by axiom 7 (ax2) }
% 0.04/0.25 ifeq2(ifeq(true, true, sorti1(j(op2(u, v))), true), true, op2(h(j(op2(u, v))), h(j(v))), h(j(u)))
% 0.04/0.25 = { by axiom 4 (ifeq_axiom) }
% 0.04/0.25 ifeq2(sorti1(j(op2(u, v))), true, op2(h(j(op2(u, v))), h(j(v))), h(j(u)))
% 0.04/0.25 = { by axiom 3 (ifeq_axiom) R->L }
% 0.04/0.25 ifeq2(true, true, ifeq2(sorti1(j(op2(u, v))), true, op2(h(j(op2(u, v))), h(j(v))), h(j(u))), h(op1(j(op2(u, v)), j(v))))
% 0.04/0.25 = { by axiom 6 (co1_3) R->L }
% 0.04/0.25 ifeq2(ifeq(sorti2(v), true, sorti1(j(v)), true), true, ifeq2(sorti1(j(op2(u, v))), true, op2(h(j(op2(u, v))), h(j(v))), h(j(u))), h(op1(j(op2(u, v)), j(v))))
% 0.04/0.25 = { by axiom 1 (ax4_1) }
% 0.04/0.25 ifeq2(ifeq(true, true, sorti1(j(v)), true), true, ifeq2(sorti1(j(op2(u, v))), true, op2(h(j(op2(u, v))), h(j(v))), h(j(u))), h(op1(j(op2(u, v)), j(v))))
% 0.04/0.25 = { by axiom 4 (ifeq_axiom) }
% 0.04/0.25 ifeq2(sorti1(j(v)), true, ifeq2(sorti1(j(op2(u, v))), true, op2(h(j(op2(u, v))), h(j(v))), h(j(u))), h(op1(j(op2(u, v)), j(v))))
% 0.04/0.25 = { by lemma 11 R->L }
% 0.04/0.25 ifeq2(sorti1(j(v)), true, ifeq2(sorti1(j(op2(u, v))), true, op2(h(j(op2(u, v))), h(j(v))), h(op1(j(op2(u, v)), j(v)))), h(op1(j(op2(u, v)), j(v))))
% 0.04/0.25 = { by axiom 10 (co1_1) }
% 0.04/0.25 h(op1(j(op2(u, v)), j(v)))
% 0.04/0.25 = { by lemma 11 }
% 0.04/0.25 h(j(u))
% 0.04/0.25 = { by axiom 3 (ifeq_axiom) R->L }
% 0.04/0.25 ifeq2(true, true, h(j(u)), u)
% 0.04/0.25 = { by axiom 2 (ax4) R->L }
% 0.04/0.25 ifeq2(sorti2(u), true, h(j(u)), u)
% 0.04/0.25 = { by axiom 5 (co1_5) }
% 0.04/0.25 u
% 0.04/0.25 % SZS output end Proof
% 0.04/0.25
% 0.04/0.25 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------