TSTP Solution File: ROB015-10 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : ROB015-10 : TPTP v8.1.2. Released v7.5.0.
% 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 : n006.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 : Thu Aug 31 14:09:09 EDT 2023
% Result : Unsatisfiable 13.84s 2.22s
% Output : Proof 13.84s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ROB015-10 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n006.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 06:44:51 EDT 2023
% 0.14/0.34 % CPUTime :
% 13.84/2.22 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 13.84/2.22
% 13.84/2.22 % SZS status Unsatisfiable
% 13.84/2.23
% 13.84/2.23 % SZS output start Proof
% 13.84/2.23 Axiom 1 (k_positive): positive_integer(k) = true.
% 13.84/2.23 Axiom 2 (commutativity_of_add): add(X, Y) = add(Y, X).
% 13.84/2.23 Axiom 3 (ifeq_axiom): ifeq4(X, X, Y, Z) = Y.
% 13.84/2.23 Axiom 4 (ifeq_axiom_001): ifeq3(X, X, Y, Z) = Y.
% 13.84/2.23 Axiom 5 (ifeq_axiom_002): ifeq2(X, X, Y, Z) = Y.
% 13.84/2.23 Axiom 6 (condition): negate(add(negate(e), negate(add(d, negate(e))))) = d.
% 13.84/2.23 Axiom 7 (lemma_3_2): ifeq4(negate(add(X, negate(add(Y, Z)))), negate(add(Y, negate(add(X, Z)))), X, Y) = Y.
% 13.84/2.23 Axiom 8 (base_step): ifeq3(negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(e), a, b) = b.
% 13.84/2.23 Axiom 9 (lemma_3_4): ifeq2(positive_integer(X), true, ifeq4(negate(add(Y, negate(Z))), W, negate(add(Y, negate(add(Z, multiply(X, add(Y, W)))))), W), W) = W.
% 13.84/2.23
% 13.84/2.23 Lemma 10: ifeq4(negate(add(X, negate(Y))), Z, negate(add(X, negate(add(Y, multiply(k, add(X, Z)))))), Z) = Z.
% 13.84/2.23 Proof:
% 13.84/2.23 ifeq4(negate(add(X, negate(Y))), Z, negate(add(X, negate(add(Y, multiply(k, add(X, Z)))))), Z)
% 13.84/2.23 = { by axiom 5 (ifeq_axiom_002) R->L }
% 13.84/2.23 ifeq2(true, true, ifeq4(negate(add(X, negate(Y))), Z, negate(add(X, negate(add(Y, multiply(k, add(X, Z)))))), Z), Z)
% 13.84/2.23 = { by axiom 1 (k_positive) R->L }
% 13.84/2.23 ifeq2(positive_integer(k), true, ifeq4(negate(add(X, negate(Y))), Z, negate(add(X, negate(add(Y, multiply(k, add(X, Z)))))), Z), Z)
% 13.84/2.23 = { by axiom 9 (lemma_3_4) }
% 13.84/2.23 Z
% 13.84/2.23
% 13.84/2.25 Goal 1 (goal): a = b.
% 13.84/2.25 Proof:
% 13.84/2.25 a
% 13.84/2.25 = { by axiom 4 (ifeq_axiom_001) R->L }
% 13.84/2.25 ifeq3(negate(e), negate(e), a, b)
% 13.84/2.25 = { by axiom 7 (lemma_3_2) R->L }
% 13.84/2.25 ifeq3(ifeq4(negate(add(negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(add(negate(e), d)))), negate(add(negate(e), negate(add(negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), d)))), negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(e)), negate(e), a, b)
% 13.84/2.25 = { by axiom 2 (commutativity_of_add) }
% 13.84/2.25 ifeq3(ifeq4(negate(add(negate(add(negate(e), d)), negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))))), negate(add(negate(e), negate(add(negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), d)))), negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(e)), negate(e), a, b)
% 13.84/2.25 = { by axiom 2 (commutativity_of_add) }
% 13.84/2.25 ifeq3(ifeq4(negate(add(negate(add(d, negate(e))), negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))))), negate(add(negate(e), negate(add(negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), d)))), negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(e)), negate(e), a, b)
% 13.84/2.25 = { by axiom 2 (commutativity_of_add) }
% 13.84/2.25 ifeq3(ifeq4(negate(add(negate(add(d, negate(e))), negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))))), negate(add(negate(e), negate(add(d, negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))))))), negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(e)), negate(e), a, b)
% 13.84/2.25 = { by axiom 3 (ifeq_axiom) R->L }
% 13.84/2.25 ifeq3(ifeq4(ifeq4(d, d, negate(add(negate(add(d, negate(e))), negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))))), d), negate(add(negate(e), negate(add(d, negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))))))), negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(e)), negate(e), a, b)
% 13.84/2.25 = { by axiom 2 (commutativity_of_add) R->L }
% 13.84/2.25 ifeq3(ifeq4(ifeq4(d, d, negate(add(negate(add(d, negate(e))), negate(add(e, multiply(k, add(negate(add(d, negate(e))), d)))))), d), negate(add(negate(e), negate(add(d, negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))))))), negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(e)), negate(e), a, b)
% 13.84/2.25 = { by axiom 6 (condition) R->L }
% 13.84/2.25 ifeq3(ifeq4(ifeq4(negate(add(negate(e), negate(add(d, negate(e))))), d, negate(add(negate(add(d, negate(e))), negate(add(e, multiply(k, add(negate(add(d, negate(e))), d)))))), d), negate(add(negate(e), negate(add(d, negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))))))), negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(e)), negate(e), a, b)
% 13.84/2.25 = { by axiom 2 (commutativity_of_add) R->L }
% 13.84/2.25 ifeq3(ifeq4(ifeq4(negate(add(negate(add(d, negate(e))), negate(e))), d, negate(add(negate(add(d, negate(e))), negate(add(e, multiply(k, add(negate(add(d, negate(e))), d)))))), d), negate(add(negate(e), negate(add(d, negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))))))), negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(e)), negate(e), a, b)
% 13.84/2.25 = { by lemma 10 }
% 13.84/2.25 ifeq3(ifeq4(d, negate(add(negate(e), negate(add(d, negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))))))), negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(e)), negate(e), a, b)
% 13.84/2.25 = { by axiom 3 (ifeq_axiom) R->L }
% 13.84/2.25 ifeq3(ifeq4(d, negate(add(negate(e), ifeq4(negate(add(d, negate(e))), negate(add(d, negate(e))), negate(add(d, negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))))), negate(add(d, negate(e)))))), negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(e)), negate(e), a, b)
% 13.84/2.25 = { by lemma 10 }
% 13.84/2.25 ifeq3(ifeq4(d, negate(add(negate(e), negate(add(d, negate(e))))), negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(e)), negate(e), a, b)
% 13.84/2.25 = { by axiom 6 (condition) }
% 13.84/2.25 ifeq3(ifeq4(d, d, negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(e)), negate(e), a, b)
% 13.84/2.25 = { by axiom 3 (ifeq_axiom) }
% 13.84/2.25 ifeq3(negate(add(e, multiply(k, add(d, negate(add(d, negate(e))))))), negate(e), a, b)
% 13.84/2.25 = { by axiom 8 (base_step) }
% 13.84/2.25 b
% 13.84/2.25 % SZS output end Proof
% 13.84/2.25
% 13.84/2.25 RESULT: Unsatisfiable (the axioms are contradictory).
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