TSTP Solution File: ALG069-10 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ALG069-10 : 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 : n017.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 16:42:09 EDT 2023
% Result : Unsatisfiable 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG069-10 : TPTP v8.1.2. Released v7.3.0.
% 0.11/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 03:09:57 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.39 Command-line arguments: --no-flatten-goal
% 0.19/0.39
% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.39
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 Axiom 1 (ax4): sorti2(sK1_ax4_U) = true.
% 0.19/0.39 Axiom 2 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.19/0.39 Axiom 3 (ifeq_axiom_001): ifeq(X, X, Y, Z) = Y.
% 0.19/0.39 Axiom 4 (co1_5): ifeq2(sorti2(X), true, h(j(X)), X) = X.
% 0.19/0.39 Axiom 5 (co1_3): ifeq(sorti2(X), true, sorti1(j(X)), true) = true.
% 0.19/0.40 Axiom 6 (co1): ifeq(sorti1(X), true, sorti2(h(X)), true) = true.
% 0.19/0.40 Axiom 7 (ax3_1): ifeq(sorti1(X), true, sorti1(sK2_ax3_V(X)), true) = true.
% 0.19/0.40 Axiom 8 (ax3): ifeq2(sorti1(X), true, op1(sK2_ax3_V(X), sK2_ax3_V(X)), X) = X.
% 0.19/0.40 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)).
% 0.19/0.40
% 0.19/0.40 Lemma 10: sorti1(j(sK1_ax4_U)) = true.
% 0.19/0.40 Proof:
% 0.19/0.40 sorti1(j(sK1_ax4_U))
% 0.19/0.40 = { by axiom 3 (ifeq_axiom_001) R->L }
% 0.19/0.40 ifeq(true, true, sorti1(j(sK1_ax4_U)), true)
% 0.19/0.40 = { by axiom 1 (ax4) R->L }
% 0.19/0.40 ifeq(sorti2(sK1_ax4_U), true, sorti1(j(sK1_ax4_U)), true)
% 0.19/0.40 = { by axiom 5 (co1_3) }
% 0.19/0.40 true
% 0.19/0.40
% 0.19/0.40 Lemma 11: sorti1(sK2_ax3_V(j(sK1_ax4_U))) = true.
% 0.19/0.40 Proof:
% 0.19/0.40 sorti1(sK2_ax3_V(j(sK1_ax4_U)))
% 0.19/0.40 = { by axiom 3 (ifeq_axiom_001) R->L }
% 0.19/0.40 ifeq(true, true, sorti1(sK2_ax3_V(j(sK1_ax4_U))), true)
% 0.19/0.40 = { by lemma 10 R->L }
% 0.19/0.40 ifeq(sorti1(j(sK1_ax4_U)), true, sorti1(sK2_ax3_V(j(sK1_ax4_U))), true)
% 0.19/0.40 = { by axiom 7 (ax3_1) }
% 0.19/0.40 true
% 0.19/0.40
% 0.19/0.40 Lemma 12: op1(sK2_ax3_V(j(sK1_ax4_U)), sK2_ax3_V(j(sK1_ax4_U))) = j(sK1_ax4_U).
% 0.19/0.40 Proof:
% 0.19/0.40 op1(sK2_ax3_V(j(sK1_ax4_U)), sK2_ax3_V(j(sK1_ax4_U)))
% 0.19/0.40 = { by axiom 2 (ifeq_axiom) R->L }
% 0.19/0.40 ifeq2(true, true, op1(sK2_ax3_V(j(sK1_ax4_U)), sK2_ax3_V(j(sK1_ax4_U))), j(sK1_ax4_U))
% 0.19/0.40 = { by lemma 10 R->L }
% 0.19/0.40 ifeq2(sorti1(j(sK1_ax4_U)), true, op1(sK2_ax3_V(j(sK1_ax4_U)), sK2_ax3_V(j(sK1_ax4_U))), j(sK1_ax4_U))
% 0.19/0.40 = { by axiom 8 (ax3) }
% 0.19/0.40 j(sK1_ax4_U)
% 0.19/0.40
% 0.19/0.40 Goal 1 (ax4_1): tuple(op2(X, X), sorti2(X)) = tuple(sK1_ax4_U, true).
% 0.19/0.40 The goal is true when:
% 0.19/0.40 X = h(sK2_ax3_V(j(sK1_ax4_U)))
% 0.19/0.40
% 0.19/0.40 Proof:
% 0.19/0.40 tuple(op2(h(sK2_ax3_V(j(sK1_ax4_U))), h(sK2_ax3_V(j(sK1_ax4_U)))), sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))))
% 0.19/0.40 = { by axiom 2 (ifeq_axiom) R->L }
% 0.19/0.40 tuple(ifeq2(true, true, op2(h(sK2_ax3_V(j(sK1_ax4_U))), h(sK2_ax3_V(j(sK1_ax4_U)))), h(j(sK1_ax4_U))), sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))))
% 0.19/0.40 = { by axiom 2 (ifeq_axiom) R->L }
% 0.19/0.40 tuple(ifeq2(true, true, ifeq2(true, true, op2(h(sK2_ax3_V(j(sK1_ax4_U))), h(sK2_ax3_V(j(sK1_ax4_U)))), h(j(sK1_ax4_U))), h(op1(sK2_ax3_V(j(sK1_ax4_U)), sK2_ax3_V(j(sK1_ax4_U))))), sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))))
% 0.19/0.40 = { by lemma 11 R->L }
% 0.19/0.40 tuple(ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))), true, ifeq2(true, true, op2(h(sK2_ax3_V(j(sK1_ax4_U))), h(sK2_ax3_V(j(sK1_ax4_U)))), h(j(sK1_ax4_U))), h(op1(sK2_ax3_V(j(sK1_ax4_U)), sK2_ax3_V(j(sK1_ax4_U))))), sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))))
% 0.19/0.40 = { by lemma 11 R->L }
% 0.19/0.40 tuple(ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))), true, ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))), true, op2(h(sK2_ax3_V(j(sK1_ax4_U))), h(sK2_ax3_V(j(sK1_ax4_U)))), h(j(sK1_ax4_U))), h(op1(sK2_ax3_V(j(sK1_ax4_U)), sK2_ax3_V(j(sK1_ax4_U))))), sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))))
% 0.19/0.40 = { by lemma 12 R->L }
% 0.19/0.40 tuple(ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))), true, ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))), true, op2(h(sK2_ax3_V(j(sK1_ax4_U))), h(sK2_ax3_V(j(sK1_ax4_U)))), h(op1(sK2_ax3_V(j(sK1_ax4_U)), sK2_ax3_V(j(sK1_ax4_U))))), h(op1(sK2_ax3_V(j(sK1_ax4_U)), sK2_ax3_V(j(sK1_ax4_U))))), sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))))
% 0.19/0.40 = { by axiom 9 (co1_1) }
% 0.19/0.40 tuple(h(op1(sK2_ax3_V(j(sK1_ax4_U)), sK2_ax3_V(j(sK1_ax4_U)))), sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))))
% 0.19/0.40 = { by lemma 12 }
% 0.19/0.40 tuple(h(j(sK1_ax4_U)), sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))))
% 0.19/0.40 = { by axiom 2 (ifeq_axiom) R->L }
% 0.19/0.40 tuple(ifeq2(true, true, h(j(sK1_ax4_U)), sK1_ax4_U), sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))))
% 0.19/0.40 = { by axiom 1 (ax4) R->L }
% 0.19/0.40 tuple(ifeq2(sorti2(sK1_ax4_U), true, h(j(sK1_ax4_U)), sK1_ax4_U), sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))))
% 0.19/0.40 = { by axiom 4 (co1_5) }
% 0.19/0.40 tuple(sK1_ax4_U, sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))))
% 0.19/0.40 = { by axiom 3 (ifeq_axiom_001) R->L }
% 0.19/0.40 tuple(sK1_ax4_U, ifeq(true, true, sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))), true))
% 0.19/0.40 = { by lemma 11 R->L }
% 0.19/0.40 tuple(sK1_ax4_U, ifeq(sorti1(sK2_ax3_V(j(sK1_ax4_U))), true, sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))), true))
% 0.19/0.40 = { by axiom 6 (co1) }
% 0.19/0.40 tuple(sK1_ax4_U, true)
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40
% 0.19/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
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