TSTP Solution File: GRP048-10 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP048-10 : 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 : n014.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 01:16:46 EDT 2023
% Result : Unsatisfiable 5.37s 1.10s
% Output : Proof 5.37s
% 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 : GRP048-10 : 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
% 0.17/0.35 % Computer : n014.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 20:11:15 EDT 2023
% 0.17/0.35 % CPUTime :
% 5.37/1.10 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 5.37/1.10
% 5.37/1.10 % SZS status Unsatisfiable
% 5.37/1.10
% 5.37/1.11 % SZS output start Proof
% 5.37/1.11 Axiom 1 (a_equals_b): equalish(a, b) = true.
% 5.37/1.11 Axiom 2 (left_identity): product(identity, X, X) = true.
% 5.37/1.11 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 5.37/1.11 Axiom 4 (left_inverse): product(inverse(X), X, identity) = true.
% 5.37/1.11 Axiom 5 (total_function1): product(X, Y, multiply(X, Y)) = true.
% 5.37/1.11 Axiom 6 (product_substitution3): ifeq(equalish(X, Y), true, ifeq(product(Z, W, X), true, product(Z, W, Y), true), true) = true.
% 5.37/1.11 Axiom 7 (total_function2): ifeq(product(X, Y, Z), true, ifeq(product(X, Y, W), true, equalish(W, Z), true), true) = true.
% 5.37/1.11 Axiom 8 (associativity1): ifeq(product(X, Y, Z), true, ifeq(product(W, Y, V), true, ifeq(product(U, W, X), true, product(U, V, Z), true), true), true) = true.
% 5.37/1.11
% 5.37/1.11 Lemma 9: ifeq(product(X, Y, Z), true, ifeq(product(W, X, identity), true, product(W, Z, Y), true), true) = true.
% 5.37/1.11 Proof:
% 5.37/1.11 ifeq(product(X, Y, Z), true, ifeq(product(W, X, identity), true, product(W, Z, Y), true), true)
% 5.37/1.11 = { by axiom 3 (ifeq_axiom) R->L }
% 5.37/1.11 ifeq(true, true, ifeq(product(X, Y, Z), true, ifeq(product(W, X, identity), true, product(W, Z, Y), true), true), true)
% 5.37/1.11 = { by axiom 2 (left_identity) R->L }
% 5.37/1.11 ifeq(product(identity, Y, Y), true, ifeq(product(X, Y, Z), true, ifeq(product(W, X, identity), true, product(W, Z, Y), true), true), true)
% 5.37/1.11 = { by axiom 8 (associativity1) }
% 5.37/1.11 true
% 5.37/1.11
% 5.37/1.11 Lemma 10: ifeq(product(X, Y, Z), true, product(inverse(X), Z, Y), true) = true.
% 5.37/1.11 Proof:
% 5.37/1.11 ifeq(product(X, Y, Z), true, product(inverse(X), Z, Y), true)
% 5.37/1.11 = { by axiom 3 (ifeq_axiom) R->L }
% 5.37/1.11 ifeq(product(X, Y, Z), true, ifeq(true, true, product(inverse(X), Z, Y), true), true)
% 5.37/1.11 = { by axiom 4 (left_inverse) R->L }
% 5.37/1.11 ifeq(product(X, Y, Z), true, ifeq(product(inverse(X), X, identity), true, product(inverse(X), Z, Y), true), true)
% 5.37/1.11 = { by lemma 9 }
% 5.37/1.11 true
% 5.37/1.11
% 5.37/1.11 Lemma 11: ifeq(product(X, inverse(Y), identity), true, product(X, identity, Y), true) = true.
% 5.37/1.11 Proof:
% 5.37/1.11 ifeq(product(X, inverse(Y), identity), true, product(X, identity, Y), true)
% 5.37/1.11 = { by axiom 3 (ifeq_axiom) R->L }
% 5.37/1.12 ifeq(true, true, ifeq(product(X, inverse(Y), identity), true, product(X, identity, Y), true), true)
% 5.37/1.12 = { by axiom 4 (left_inverse) R->L }
% 5.37/1.12 ifeq(product(inverse(Y), Y, identity), true, ifeq(product(X, inverse(Y), identity), true, product(X, identity, Y), true), true)
% 5.37/1.12 = { by lemma 9 }
% 5.37/1.12 true
% 5.37/1.12
% 5.37/1.12 Lemma 12: product(X, identity, X) = true.
% 5.37/1.12 Proof:
% 5.37/1.12 product(X, identity, X)
% 5.37/1.12 = { by axiom 3 (ifeq_axiom) R->L }
% 5.37/1.12 ifeq(true, true, product(X, identity, X), true)
% 5.37/1.12 = { by axiom 6 (product_substitution3) R->L }
% 5.37/1.12 ifeq(ifeq(equalish(multiply(X, inverse(X)), identity), true, ifeq(product(X, inverse(X), multiply(X, inverse(X))), true, product(X, inverse(X), identity), true), true), true, product(X, identity, X), true)
% 5.37/1.12 = { by axiom 5 (total_function1) }
% 5.37/1.12 ifeq(ifeq(equalish(multiply(X, inverse(X)), identity), true, ifeq(true, true, product(X, inverse(X), identity), true), true), true, product(X, identity, X), true)
% 5.37/1.12 = { by axiom 3 (ifeq_axiom) }
% 5.37/1.12 ifeq(ifeq(equalish(multiply(X, inverse(X)), identity), true, product(X, inverse(X), identity), true), true, product(X, identity, X), true)
% 5.37/1.12 = { by axiom 3 (ifeq_axiom) R->L }
% 5.37/1.12 ifeq(ifeq(ifeq(true, true, equalish(multiply(X, inverse(X)), identity), true), true, product(X, inverse(X), identity), true), true, product(X, identity, X), true)
% 5.37/1.12 = { by lemma 10 R->L }
% 5.37/1.12 ifeq(ifeq(ifeq(ifeq(product(inverse(X), multiply(X, inverse(X)), inverse(X)), true, product(inverse(inverse(X)), inverse(X), multiply(X, inverse(X))), true), true, equalish(multiply(X, inverse(X)), identity), true), true, product(X, inverse(X), identity), true), true, product(X, identity, X), true)
% 5.37/1.12 = { by axiom 3 (ifeq_axiom) R->L }
% 5.37/1.12 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, product(inverse(X), multiply(X, inverse(X)), inverse(X)), true), true, product(inverse(inverse(X)), inverse(X), multiply(X, inverse(X))), true), true, equalish(multiply(X, inverse(X)), identity), true), true, product(X, inverse(X), identity), true), true, product(X, identity, X), true)
% 5.37/1.12 = { by axiom 5 (total_function1) R->L }
% 5.37/1.12 ifeq(ifeq(ifeq(ifeq(ifeq(product(X, inverse(X), multiply(X, inverse(X))), true, product(inverse(X), multiply(X, inverse(X)), inverse(X)), true), true, product(inverse(inverse(X)), inverse(X), multiply(X, inverse(X))), true), true, equalish(multiply(X, inverse(X)), identity), true), true, product(X, inverse(X), identity), true), true, product(X, identity, X), true)
% 5.37/1.12 = { by lemma 10 }
% 5.37/1.12 ifeq(ifeq(ifeq(ifeq(true, true, product(inverse(inverse(X)), inverse(X), multiply(X, inverse(X))), true), true, equalish(multiply(X, inverse(X)), identity), true), true, product(X, inverse(X), identity), true), true, product(X, identity, X), true)
% 5.37/1.12 = { by axiom 3 (ifeq_axiom) }
% 5.37/1.12 ifeq(ifeq(ifeq(product(inverse(inverse(X)), inverse(X), multiply(X, inverse(X))), true, equalish(multiply(X, inverse(X)), identity), true), true, product(X, inverse(X), identity), true), true, product(X, identity, X), true)
% 5.37/1.12 = { by axiom 3 (ifeq_axiom) R->L }
% 5.37/1.12 ifeq(ifeq(ifeq(true, true, ifeq(product(inverse(inverse(X)), inverse(X), multiply(X, inverse(X))), true, equalish(multiply(X, inverse(X)), identity), true), true), true, product(X, inverse(X), identity), true), true, product(X, identity, X), true)
% 5.37/1.12 = { by axiom 4 (left_inverse) R->L }
% 5.37/1.12 ifeq(ifeq(ifeq(product(inverse(inverse(X)), inverse(X), identity), true, ifeq(product(inverse(inverse(X)), inverse(X), multiply(X, inverse(X))), true, equalish(multiply(X, inverse(X)), identity), true), true), true, product(X, inverse(X), identity), true), true, product(X, identity, X), true)
% 5.37/1.12 = { by axiom 7 (total_function2) }
% 5.37/1.12 ifeq(ifeq(true, true, product(X, inverse(X), identity), true), true, product(X, identity, X), true)
% 5.37/1.12 = { by axiom 3 (ifeq_axiom) }
% 5.37/1.12 ifeq(product(X, inverse(X), identity), true, product(X, identity, X), true)
% 5.37/1.12 = { by lemma 11 }
% 5.37/1.12 true
% 5.37/1.12
% 5.37/1.12 Lemma 13: ifeq(product(X, identity, Y), true, equalish(Y, X), true) = true.
% 5.37/1.12 Proof:
% 5.37/1.12 ifeq(product(X, identity, Y), true, equalish(Y, X), true)
% 5.37/1.12 = { by axiom 3 (ifeq_axiom) R->L }
% 5.37/1.12 ifeq(true, true, ifeq(product(X, identity, Y), true, equalish(Y, X), true), true)
% 5.37/1.12 = { by lemma 12 R->L }
% 5.37/1.12 ifeq(product(X, identity, X), true, ifeq(product(X, identity, Y), true, equalish(Y, X), true), true)
% 5.37/1.12 = { by axiom 7 (total_function2) }
% 5.37/1.12 true
% 5.37/1.12
% 5.37/1.12 Goal 1 (prove_inverse_substitution): equalish(inverse(a), inverse(b)) = true.
% 5.37/1.12 Proof:
% 5.37/1.12 equalish(inverse(a), inverse(b))
% 5.37/1.12 = { by axiom 3 (ifeq_axiom) R->L }
% 5.37/1.12 ifeq(true, true, equalish(inverse(a), inverse(b)), true)
% 5.37/1.12 = { by lemma 11 R->L }
% 5.37/1.12 ifeq(ifeq(product(inverse(b), inverse(inverse(a)), identity), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true)
% 5.37/1.12 = { by axiom 3 (ifeq_axiom) R->L }
% 5.37/1.12 ifeq(ifeq(ifeq(true, true, product(inverse(b), inverse(inverse(a)), identity), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true)
% 5.37/1.12 = { by axiom 6 (product_substitution3) R->L }
% 5.37/1.12 ifeq(ifeq(ifeq(ifeq(equalish(b, inverse(inverse(a))), true, ifeq(product(b, identity, b), true, product(b, identity, inverse(inverse(a))), true), true), true, product(inverse(b), inverse(inverse(a)), identity), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true)
% 5.37/1.12 = { by lemma 12 }
% 5.37/1.12 ifeq(ifeq(ifeq(ifeq(equalish(b, inverse(inverse(a))), true, ifeq(true, true, product(b, identity, inverse(inverse(a))), true), true), true, product(inverse(b), inverse(inverse(a)), identity), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true)
% 5.37/1.12 = { by axiom 3 (ifeq_axiom) }
% 5.37/1.12 ifeq(ifeq(ifeq(ifeq(equalish(b, inverse(inverse(a))), true, product(b, identity, inverse(inverse(a))), true), true, product(inverse(b), inverse(inverse(a)), identity), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true)
% 5.37/1.12 = { by axiom 3 (ifeq_axiom) R->L }
% 5.37/1.12 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, equalish(b, inverse(inverse(a))), true), true, product(b, identity, inverse(inverse(a))), true), true, product(inverse(b), inverse(inverse(a)), identity), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true)
% 5.37/1.12 = { by axiom 6 (product_substitution3) R->L }
% 5.37/1.12 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(equalish(a, b), true, ifeq(product(inverse(inverse(a)), identity, a), true, product(inverse(inverse(a)), identity, b), true), true), true, equalish(b, inverse(inverse(a))), true), true, product(b, identity, inverse(inverse(a))), true), true, product(inverse(b), inverse(inverse(a)), identity), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true)
% 5.37/1.12 = { by axiom 1 (a_equals_b) }
% 5.37/1.12 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(product(inverse(inverse(a)), identity, a), true, product(inverse(inverse(a)), identity, b), true), true), true, equalish(b, inverse(inverse(a))), true), true, product(b, identity, inverse(inverse(a))), true), true, product(inverse(b), inverse(inverse(a)), identity), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true)
% 5.37/1.12 = { by axiom 3 (ifeq_axiom) }
% 5.37/1.12 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(product(inverse(inverse(a)), identity, a), true, product(inverse(inverse(a)), identity, b), true), true, equalish(b, inverse(inverse(a))), true), true, product(b, identity, inverse(inverse(a))), true), true, product(inverse(b), inverse(inverse(a)), identity), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true)
% 5.37/1.12 = { by axiom 3 (ifeq_axiom) R->L }
% 5.37/1.12 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, product(inverse(inverse(a)), identity, a), true), true, product(inverse(inverse(a)), identity, b), true), true, equalish(b, inverse(inverse(a))), true), true, product(b, identity, inverse(inverse(a))), true), true, product(inverse(b), inverse(inverse(a)), identity), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true)
% 5.37/1.12 = { by axiom 4 (left_inverse) R->L }
% 5.37/1.12 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(product(inverse(a), a, identity), true, product(inverse(inverse(a)), identity, a), true), true, product(inverse(inverse(a)), identity, b), true), true, equalish(b, inverse(inverse(a))), true), true, product(b, identity, inverse(inverse(a))), true), true, product(inverse(b), inverse(inverse(a)), identity), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true)
% 5.37/1.12 = { by lemma 10 }
% 5.37/1.12 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, product(inverse(inverse(a)), identity, b), true), true, equalish(b, inverse(inverse(a))), true), true, product(b, identity, inverse(inverse(a))), true), true, product(inverse(b), inverse(inverse(a)), identity), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true)
% 5.37/1.12 = { by axiom 3 (ifeq_axiom) }
% 5.37/1.12 ifeq(ifeq(ifeq(ifeq(ifeq(product(inverse(inverse(a)), identity, b), true, equalish(b, inverse(inverse(a))), true), true, product(b, identity, inverse(inverse(a))), true), true, product(inverse(b), inverse(inverse(a)), identity), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true)
% 5.37/1.12 = { by lemma 13 }
% 5.37/1.12 ifeq(ifeq(ifeq(ifeq(true, true, product(b, identity, inverse(inverse(a))), true), true, product(inverse(b), inverse(inverse(a)), identity), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true)
% 5.37/1.12 = { by axiom 3 (ifeq_axiom) }
% 5.37/1.12 ifeq(ifeq(ifeq(product(b, identity, inverse(inverse(a))), true, product(inverse(b), inverse(inverse(a)), identity), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true)
% 5.37/1.12 = { by lemma 10 }
% 5.37/1.12 ifeq(ifeq(true, true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true)
% 5.37/1.12 = { by axiom 3 (ifeq_axiom) }
% 5.37/1.12 ifeq(product(inverse(b), identity, inverse(a)), true, equalish(inverse(a), inverse(b)), true)
% 5.37/1.12 = { by lemma 13 }
% 5.37/1.12 true
% 5.37/1.12 % SZS output end Proof
% 5.37/1.12
% 5.37/1.12 RESULT: Unsatisfiable (the axioms are contradictory).
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