TSTP Solution File: ALG030-10 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ALG030-10 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 16:42:03 EDT 2023
% Result : Unsatisfiable 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ALG030-10 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.17/0.35 % Computer : n012.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Mon Aug 28 05:06:25 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.21/0.40 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.40
% 0.21/0.40 % SZS status Unsatisfiable
% 0.21/0.40
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 Axiom 1 (ax3): sorti1(sK2_ax3_U) = true.
% 0.21/0.41 Axiom 2 (ax3_1): sorti1(sK1_ax3_V) = true.
% 0.21/0.41 Axiom 3 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.21/0.41 Axiom 4 (ifeq_axiom_001): ifeq(X, X, Y, Z) = Y.
% 0.21/0.41 Axiom 5 (co1_2): ifeq2(sorti1(X), true, j(h(X)), X) = X.
% 0.21/0.41 Axiom 6 (co1): ifeq(sorti1(X), true, sorti2(h(X)), true) = true.
% 0.21/0.41 Axiom 7 (ax1): ifeq(sorti1(X), true, ifeq(sorti1(Y), true, sorti1(op1(Y, X)), true), true) = true.
% 0.21/0.41 Axiom 8 (ax4): ifeq2(sorti2(X), true, ifeq2(sorti2(Y), true, op2(Y, X), op2(X, Y)), op2(X, Y)) = op2(X, Y).
% 0.21/0.41 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)).
% 0.21/0.41
% 0.21/0.41 Goal 1 (ax3_2): op1(sK2_ax3_U, sK1_ax3_V) = op1(sK1_ax3_V, sK2_ax3_U).
% 0.21/0.41 Proof:
% 0.21/0.41 op1(sK2_ax3_U, sK1_ax3_V)
% 0.21/0.41 = { by axiom 5 (co1_2) R->L }
% 0.21/0.41 ifeq2(sorti1(op1(sK2_ax3_U, sK1_ax3_V)), true, j(h(op1(sK2_ax3_U, sK1_ax3_V))), op1(sK2_ax3_U, sK1_ax3_V))
% 0.21/0.41 = { by axiom 4 (ifeq_axiom_001) R->L }
% 0.21/0.41 ifeq2(ifeq(true, true, sorti1(op1(sK2_ax3_U, sK1_ax3_V)), true), true, j(h(op1(sK2_ax3_U, sK1_ax3_V))), op1(sK2_ax3_U, sK1_ax3_V))
% 0.21/0.41 = { by axiom 1 (ax3) R->L }
% 0.21/0.41 ifeq2(ifeq(sorti1(sK2_ax3_U), true, sorti1(op1(sK2_ax3_U, sK1_ax3_V)), true), true, j(h(op1(sK2_ax3_U, sK1_ax3_V))), op1(sK2_ax3_U, sK1_ax3_V))
% 0.21/0.41 = { by axiom 4 (ifeq_axiom_001) R->L }
% 0.21/0.41 ifeq2(ifeq(true, true, ifeq(sorti1(sK2_ax3_U), true, sorti1(op1(sK2_ax3_U, sK1_ax3_V)), true), true), true, j(h(op1(sK2_ax3_U, sK1_ax3_V))), op1(sK2_ax3_U, sK1_ax3_V))
% 0.21/0.41 = { by axiom 2 (ax3_1) R->L }
% 0.21/0.41 ifeq2(ifeq(sorti1(sK1_ax3_V), true, ifeq(sorti1(sK2_ax3_U), true, sorti1(op1(sK2_ax3_U, sK1_ax3_V)), true), true), true, j(h(op1(sK2_ax3_U, sK1_ax3_V))), op1(sK2_ax3_U, sK1_ax3_V))
% 0.21/0.41 = { by axiom 7 (ax1) }
% 0.21/0.41 ifeq2(true, true, j(h(op1(sK2_ax3_U, sK1_ax3_V))), op1(sK2_ax3_U, sK1_ax3_V))
% 0.21/0.41 = { by axiom 3 (ifeq_axiom) }
% 0.21/0.41 j(h(op1(sK2_ax3_U, sK1_ax3_V)))
% 0.21/0.41 = { by axiom 3 (ifeq_axiom) R->L }
% 0.21/0.41 ifeq2(true, true, j(h(op1(sK2_ax3_U, sK1_ax3_V))), op1(sK1_ax3_V, sK2_ax3_U))
% 0.21/0.41 = { by axiom 7 (ax1) R->L }
% 0.21/0.41 ifeq2(ifeq(sorti1(sK2_ax3_U), true, ifeq(sorti1(sK1_ax3_V), true, sorti1(op1(sK1_ax3_V, sK2_ax3_U)), true), true), true, j(h(op1(sK2_ax3_U, sK1_ax3_V))), op1(sK1_ax3_V, sK2_ax3_U))
% 0.21/0.41 = { by axiom 1 (ax3) }
% 0.21/0.41 ifeq2(ifeq(true, true, ifeq(sorti1(sK1_ax3_V), true, sorti1(op1(sK1_ax3_V, sK2_ax3_U)), true), true), true, j(h(op1(sK2_ax3_U, sK1_ax3_V))), op1(sK1_ax3_V, sK2_ax3_U))
% 0.21/0.41 = { by axiom 4 (ifeq_axiom_001) }
% 0.21/0.41 ifeq2(ifeq(sorti1(sK1_ax3_V), true, sorti1(op1(sK1_ax3_V, sK2_ax3_U)), true), true, j(h(op1(sK2_ax3_U, sK1_ax3_V))), op1(sK1_ax3_V, sK2_ax3_U))
% 0.21/0.41 = { by axiom 2 (ax3_1) }
% 0.21/0.41 ifeq2(ifeq(true, true, sorti1(op1(sK1_ax3_V, sK2_ax3_U)), true), true, j(h(op1(sK2_ax3_U, sK1_ax3_V))), op1(sK1_ax3_V, sK2_ax3_U))
% 0.21/0.41 = { by axiom 4 (ifeq_axiom_001) }
% 0.21/0.41 ifeq2(sorti1(op1(sK1_ax3_V, sK2_ax3_U)), true, j(h(op1(sK2_ax3_U, sK1_ax3_V))), op1(sK1_ax3_V, sK2_ax3_U))
% 0.21/0.41 = { by axiom 9 (co1_1) R->L }
% 0.21/0.41 ifeq2(sorti1(op1(sK1_ax3_V, sK2_ax3_U)), true, j(ifeq2(sorti1(sK1_ax3_V), true, ifeq2(sorti1(sK2_ax3_U), true, op2(h(sK2_ax3_U), h(sK1_ax3_V)), h(op1(sK2_ax3_U, sK1_ax3_V))), h(op1(sK2_ax3_U, sK1_ax3_V)))), op1(sK1_ax3_V, sK2_ax3_U))
% 0.21/0.41 = { by axiom 2 (ax3_1) }
% 0.21/0.41 ifeq2(sorti1(op1(sK1_ax3_V, sK2_ax3_U)), true, j(ifeq2(true, true, ifeq2(sorti1(sK2_ax3_U), true, op2(h(sK2_ax3_U), h(sK1_ax3_V)), h(op1(sK2_ax3_U, sK1_ax3_V))), h(op1(sK2_ax3_U, sK1_ax3_V)))), op1(sK1_ax3_V, sK2_ax3_U))
% 0.21/0.41 = { by axiom 3 (ifeq_axiom) }
% 0.21/0.41 ifeq2(sorti1(op1(sK1_ax3_V, sK2_ax3_U)), true, j(ifeq2(sorti1(sK2_ax3_U), true, op2(h(sK2_ax3_U), h(sK1_ax3_V)), h(op1(sK2_ax3_U, sK1_ax3_V)))), op1(sK1_ax3_V, sK2_ax3_U))
% 0.21/0.41 = { by axiom 1 (ax3) }
% 0.21/0.41 ifeq2(sorti1(op1(sK1_ax3_V, sK2_ax3_U)), true, j(ifeq2(true, true, op2(h(sK2_ax3_U), h(sK1_ax3_V)), h(op1(sK2_ax3_U, sK1_ax3_V)))), op1(sK1_ax3_V, sK2_ax3_U))
% 0.21/0.41 = { by axiom 3 (ifeq_axiom) }
% 0.21/0.41 ifeq2(sorti1(op1(sK1_ax3_V, sK2_ax3_U)), true, j(op2(h(sK2_ax3_U), h(sK1_ax3_V))), op1(sK1_ax3_V, sK2_ax3_U))
% 0.21/0.41 = { by axiom 8 (ax4) R->L }
% 0.21/0.41 ifeq2(sorti1(op1(sK1_ax3_V, sK2_ax3_U)), true, j(ifeq2(sorti2(h(sK2_ax3_U)), true, ifeq2(sorti2(h(sK1_ax3_V)), true, op2(h(sK1_ax3_V), h(sK2_ax3_U)), op2(h(sK2_ax3_U), h(sK1_ax3_V))), op2(h(sK2_ax3_U), h(sK1_ax3_V)))), op1(sK1_ax3_V, sK2_ax3_U))
% 0.21/0.41 = { by axiom 3 (ifeq_axiom) R->L }
% 0.21/0.41 ifeq2(sorti1(op1(sK1_ax3_V, sK2_ax3_U)), true, j(ifeq2(sorti2(h(sK2_ax3_U)), true, ifeq2(sorti2(h(sK1_ax3_V)), true, ifeq2(true, true, op2(h(sK1_ax3_V), h(sK2_ax3_U)), h(op1(sK1_ax3_V, sK2_ax3_U))), op2(h(sK2_ax3_U), h(sK1_ax3_V))), op2(h(sK2_ax3_U), h(sK1_ax3_V)))), op1(sK1_ax3_V, sK2_ax3_U))
% 0.21/0.42 = { by axiom 2 (ax3_1) R->L }
% 0.21/0.42 ifeq2(sorti1(op1(sK1_ax3_V, sK2_ax3_U)), true, j(ifeq2(sorti2(h(sK2_ax3_U)), true, ifeq2(sorti2(h(sK1_ax3_V)), true, ifeq2(sorti1(sK1_ax3_V), true, op2(h(sK1_ax3_V), h(sK2_ax3_U)), h(op1(sK1_ax3_V, sK2_ax3_U))), op2(h(sK2_ax3_U), h(sK1_ax3_V))), op2(h(sK2_ax3_U), h(sK1_ax3_V)))), op1(sK1_ax3_V, sK2_ax3_U))
% 0.21/0.42 = { by axiom 3 (ifeq_axiom) R->L }
% 0.21/0.42 ifeq2(sorti1(op1(sK1_ax3_V, sK2_ax3_U)), true, j(ifeq2(sorti2(h(sK2_ax3_U)), true, ifeq2(sorti2(h(sK1_ax3_V)), true, ifeq2(true, true, ifeq2(sorti1(sK1_ax3_V), true, op2(h(sK1_ax3_V), h(sK2_ax3_U)), h(op1(sK1_ax3_V, sK2_ax3_U))), h(op1(sK1_ax3_V, sK2_ax3_U))), op2(h(sK2_ax3_U), h(sK1_ax3_V))), op2(h(sK2_ax3_U), h(sK1_ax3_V)))), op1(sK1_ax3_V, sK2_ax3_U))
% 0.21/0.42 = { by axiom 1 (ax3) R->L }
% 0.21/0.42 ifeq2(sorti1(op1(sK1_ax3_V, sK2_ax3_U)), true, j(ifeq2(sorti2(h(sK2_ax3_U)), true, ifeq2(sorti2(h(sK1_ax3_V)), true, ifeq2(sorti1(sK2_ax3_U), true, ifeq2(sorti1(sK1_ax3_V), true, op2(h(sK1_ax3_V), h(sK2_ax3_U)), h(op1(sK1_ax3_V, sK2_ax3_U))), h(op1(sK1_ax3_V, sK2_ax3_U))), op2(h(sK2_ax3_U), h(sK1_ax3_V))), op2(h(sK2_ax3_U), h(sK1_ax3_V)))), op1(sK1_ax3_V, sK2_ax3_U))
% 0.21/0.42 = { by axiom 9 (co1_1) }
% 0.21/0.42 ifeq2(sorti1(op1(sK1_ax3_V, sK2_ax3_U)), true, j(ifeq2(sorti2(h(sK2_ax3_U)), true, ifeq2(sorti2(h(sK1_ax3_V)), true, h(op1(sK1_ax3_V, sK2_ax3_U)), op2(h(sK2_ax3_U), h(sK1_ax3_V))), op2(h(sK2_ax3_U), h(sK1_ax3_V)))), op1(sK1_ax3_V, sK2_ax3_U))
% 0.21/0.42 = { by axiom 4 (ifeq_axiom_001) R->L }
% 0.21/0.42 ifeq2(sorti1(op1(sK1_ax3_V, sK2_ax3_U)), true, j(ifeq2(ifeq(true, true, sorti2(h(sK2_ax3_U)), true), true, ifeq2(sorti2(h(sK1_ax3_V)), true, h(op1(sK1_ax3_V, sK2_ax3_U)), op2(h(sK2_ax3_U), h(sK1_ax3_V))), op2(h(sK2_ax3_U), h(sK1_ax3_V)))), op1(sK1_ax3_V, sK2_ax3_U))
% 0.21/0.42 = { by axiom 1 (ax3) R->L }
% 0.21/0.42 ifeq2(sorti1(op1(sK1_ax3_V, sK2_ax3_U)), true, j(ifeq2(ifeq(sorti1(sK2_ax3_U), true, sorti2(h(sK2_ax3_U)), true), true, ifeq2(sorti2(h(sK1_ax3_V)), true, h(op1(sK1_ax3_V, sK2_ax3_U)), op2(h(sK2_ax3_U), h(sK1_ax3_V))), op2(h(sK2_ax3_U), h(sK1_ax3_V)))), op1(sK1_ax3_V, sK2_ax3_U))
% 0.21/0.42 = { by axiom 6 (co1) }
% 0.21/0.42 ifeq2(sorti1(op1(sK1_ax3_V, sK2_ax3_U)), true, j(ifeq2(true, true, ifeq2(sorti2(h(sK1_ax3_V)), true, h(op1(sK1_ax3_V, sK2_ax3_U)), op2(h(sK2_ax3_U), h(sK1_ax3_V))), op2(h(sK2_ax3_U), h(sK1_ax3_V)))), op1(sK1_ax3_V, sK2_ax3_U))
% 0.21/0.42 = { by axiom 3 (ifeq_axiom) }
% 0.21/0.42 ifeq2(sorti1(op1(sK1_ax3_V, sK2_ax3_U)), true, j(ifeq2(sorti2(h(sK1_ax3_V)), true, h(op1(sK1_ax3_V, sK2_ax3_U)), op2(h(sK2_ax3_U), h(sK1_ax3_V)))), op1(sK1_ax3_V, sK2_ax3_U))
% 0.21/0.42 = { by axiom 4 (ifeq_axiom_001) R->L }
% 0.21/0.42 ifeq2(sorti1(op1(sK1_ax3_V, sK2_ax3_U)), true, j(ifeq2(ifeq(true, true, sorti2(h(sK1_ax3_V)), true), true, h(op1(sK1_ax3_V, sK2_ax3_U)), op2(h(sK2_ax3_U), h(sK1_ax3_V)))), op1(sK1_ax3_V, sK2_ax3_U))
% 0.21/0.42 = { by axiom 2 (ax3_1) R->L }
% 0.21/0.42 ifeq2(sorti1(op1(sK1_ax3_V, sK2_ax3_U)), true, j(ifeq2(ifeq(sorti1(sK1_ax3_V), true, sorti2(h(sK1_ax3_V)), true), true, h(op1(sK1_ax3_V, sK2_ax3_U)), op2(h(sK2_ax3_U), h(sK1_ax3_V)))), op1(sK1_ax3_V, sK2_ax3_U))
% 0.21/0.42 = { by axiom 6 (co1) }
% 0.21/0.42 ifeq2(sorti1(op1(sK1_ax3_V, sK2_ax3_U)), true, j(ifeq2(true, true, h(op1(sK1_ax3_V, sK2_ax3_U)), op2(h(sK2_ax3_U), h(sK1_ax3_V)))), op1(sK1_ax3_V, sK2_ax3_U))
% 0.21/0.42 = { by axiom 3 (ifeq_axiom) }
% 0.21/0.42 ifeq2(sorti1(op1(sK1_ax3_V, sK2_ax3_U)), true, j(h(op1(sK1_ax3_V, sK2_ax3_U))), op1(sK1_ax3_V, sK2_ax3_U))
% 0.21/0.42 = { by axiom 5 (co1_2) }
% 0.21/0.42 op1(sK1_ax3_V, sK2_ax3_U)
% 0.21/0.42 % SZS output end Proof
% 0.21/0.42
% 0.21/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------