TSTP Solution File: HEN010-10 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : HEN010-10 : 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 : 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 01:57:01 EDT 2023
% Result : Unsatisfiable 39.05s 5.46s
% Output : Proof 39.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : HEN010-10 : 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
% 0.13/0.35 % Computer : n006.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 13:28:22 EDT 2023
% 0.13/0.35 % CPUTime :
% 39.05/5.46 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 39.05/5.46
% 39.05/5.46 % SZS status Unsatisfiable
% 39.05/5.46
% 39.05/5.48 % SZS output start Proof
% 39.05/5.48 Axiom 1 (identity_is_largest): less_equal(X, identity) = true.
% 39.05/5.48 Axiom 2 (x_divide_x_is_zero): quotient(X, X, zero) = true.
% 39.05/5.48 Axiom 3 (x_divde_zero_is_x): quotient(X, zero, X) = true.
% 39.05/5.48 Axiom 4 (identity_divide_idQa): quotient(identity, idQa, idQ_idQa) = true.
% 39.05/5.48 Axiom 5 (identity_divide_a): quotient(identity, a, idQa) = true.
% 39.05/5.48 Axiom 6 (identity_divide_idQ_idQa): quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa) = true.
% 39.05/5.48 Axiom 7 (ifeq_axiom_001): ifeq(X, X, Y, Z) = Y.
% 39.05/5.48 Axiom 8 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 39.05/5.48 Axiom 9 (closure): quotient(X, Y, divide(X, Y)) = true.
% 39.05/5.48 Axiom 10 (divisor_existence): ifeq(quotient(X, Y, Z), true, less_equal(Z, X), true) = true.
% 39.05/5.48 Axiom 11 (less_equal_and_equal): ifeq2(less_equal(X, Y), true, ifeq2(less_equal(Y, X), true, Y, X), X) = X.
% 39.05/5.48 Axiom 12 (well_defined): ifeq2(quotient(X, Y, Z), true, ifeq2(quotient(X, Y, W), true, W, Z), Z) = Z.
% 39.05/5.48 Axiom 13 (xLEy_implies_zQyLEzQx): ifeq(quotient(X, Y, Z), true, ifeq(quotient(X, W, V), true, ifeq(less_equal(W, Y), true, less_equal(Z, V), true), true), true) = true.
% 39.05/5.48 Axiom 14 (xQyLEz_implies_xQzLEy): ifeq(quotient(X, Y, Z), true, ifeq(quotient(X, W, V), true, ifeq(less_equal(V, Y), true, less_equal(Z, W), true), true), true) = true.
% 39.05/5.48 Axiom 15 (xLEy_implies_xQzLEyQz): ifeq(quotient(X, Y, Z), true, ifeq(quotient(W, Y, V), true, ifeq(less_equal(W, X), true, less_equal(V, Z), true), true), true) = true.
% 39.05/5.48 Axiom 16 (quotient_property): ifeq(quotient(X, Y, Z), true, ifeq(quotient(W, V, U), true, ifeq(quotient(T, V, Y), true, ifeq(quotient(S, V, X), true, ifeq(quotient(S, T, W), true, less_equal(Z, U), true), true), true), true), true) = true.
% 39.05/5.48
% 39.05/5.48 Lemma 17: divide(idQa, a) = idQa.
% 39.05/5.48 Proof:
% 39.05/5.48 divide(idQa, a)
% 39.05/5.48 = { by axiom 8 (ifeq_axiom) R->L }
% 39.05/5.48 ifeq2(true, true, divide(idQa, a), idQa)
% 39.05/5.48 = { by axiom 15 (xLEy_implies_xQzLEyQz) R->L }
% 39.05/5.48 ifeq2(ifeq(quotient(identity, a, idQa), true, ifeq(quotient(idQa, a, divide(idQa, a)), true, ifeq(less_equal(idQa, identity), true, less_equal(divide(idQa, a), idQa), true), true), true), true, divide(idQa, a), idQa)
% 39.05/5.48 = { by axiom 5 (identity_divide_a) }
% 39.05/5.48 ifeq2(ifeq(true, true, ifeq(quotient(idQa, a, divide(idQa, a)), true, ifeq(less_equal(idQa, identity), true, less_equal(divide(idQa, a), idQa), true), true), true), true, divide(idQa, a), idQa)
% 39.05/5.48 = { by axiom 7 (ifeq_axiom_001) }
% 39.05/5.48 ifeq2(ifeq(quotient(idQa, a, divide(idQa, a)), true, ifeq(less_equal(idQa, identity), true, less_equal(divide(idQa, a), idQa), true), true), true, divide(idQa, a), idQa)
% 39.05/5.48 = { by axiom 1 (identity_is_largest) }
% 39.05/5.48 ifeq2(ifeq(quotient(idQa, a, divide(idQa, a)), true, ifeq(true, true, less_equal(divide(idQa, a), idQa), true), true), true, divide(idQa, a), idQa)
% 39.05/5.48 = { by axiom 7 (ifeq_axiom_001) }
% 39.05/5.48 ifeq2(ifeq(quotient(idQa, a, divide(idQa, a)), true, less_equal(divide(idQa, a), idQa), true), true, divide(idQa, a), idQa)
% 39.05/5.48 = { by axiom 9 (closure) }
% 39.05/5.48 ifeq2(ifeq(true, true, less_equal(divide(idQa, a), idQa), true), true, divide(idQa, a), idQa)
% 39.05/5.48 = { by axiom 7 (ifeq_axiom_001) }
% 39.05/5.48 ifeq2(less_equal(divide(idQa, a), idQa), true, divide(idQa, a), idQa)
% 39.05/5.48 = { by axiom 8 (ifeq_axiom) R->L }
% 39.05/5.48 ifeq2(true, true, ifeq2(less_equal(divide(idQa, a), idQa), true, divide(idQa, a), idQa), idQa)
% 39.05/5.48 = { by axiom 16 (quotient_property) R->L }
% 39.05/5.48 ifeq2(ifeq(quotient(idQa, zero, idQa), true, ifeq(quotient(idQa, a, divide(idQa, a)), true, ifeq(quotient(a, a, zero), true, ifeq(quotient(identity, a, idQa), true, ifeq(quotient(identity, a, idQa), true, less_equal(idQa, divide(idQa, a)), true), true), true), true), true), true, ifeq2(less_equal(divide(idQa, a), idQa), true, divide(idQa, a), idQa), idQa)
% 39.05/5.48 = { by axiom 3 (x_divde_zero_is_x) }
% 39.05/5.48 ifeq2(ifeq(true, true, ifeq(quotient(idQa, a, divide(idQa, a)), true, ifeq(quotient(a, a, zero), true, ifeq(quotient(identity, a, idQa), true, ifeq(quotient(identity, a, idQa), true, less_equal(idQa, divide(idQa, a)), true), true), true), true), true), true, ifeq2(less_equal(divide(idQa, a), idQa), true, divide(idQa, a), idQa), idQa)
% 39.05/5.48 = { by axiom 7 (ifeq_axiom_001) }
% 39.05/5.48 ifeq2(ifeq(quotient(idQa, a, divide(idQa, a)), true, ifeq(quotient(a, a, zero), true, ifeq(quotient(identity, a, idQa), true, ifeq(quotient(identity, a, idQa), true, less_equal(idQa, divide(idQa, a)), true), true), true), true), true, ifeq2(less_equal(divide(idQa, a), idQa), true, divide(idQa, a), idQa), idQa)
% 39.05/5.48 = { by axiom 5 (identity_divide_a) }
% 39.05/5.48 ifeq2(ifeq(quotient(idQa, a, divide(idQa, a)), true, ifeq(quotient(a, a, zero), true, ifeq(quotient(identity, a, idQa), true, ifeq(true, true, less_equal(idQa, divide(idQa, a)), true), true), true), true), true, ifeq2(less_equal(divide(idQa, a), idQa), true, divide(idQa, a), idQa), idQa)
% 39.05/5.48 = { by axiom 7 (ifeq_axiom_001) }
% 39.05/5.48 ifeq2(ifeq(quotient(idQa, a, divide(idQa, a)), true, ifeq(quotient(a, a, zero), true, ifeq(quotient(identity, a, idQa), true, less_equal(idQa, divide(idQa, a)), true), true), true), true, ifeq2(less_equal(divide(idQa, a), idQa), true, divide(idQa, a), idQa), idQa)
% 39.05/5.48 = { by axiom 5 (identity_divide_a) }
% 39.05/5.48 ifeq2(ifeq(quotient(idQa, a, divide(idQa, a)), true, ifeq(quotient(a, a, zero), true, ifeq(true, true, less_equal(idQa, divide(idQa, a)), true), true), true), true, ifeq2(less_equal(divide(idQa, a), idQa), true, divide(idQa, a), idQa), idQa)
% 39.05/5.48 = { by axiom 2 (x_divide_x_is_zero) }
% 39.05/5.48 ifeq2(ifeq(quotient(idQa, a, divide(idQa, a)), true, ifeq(true, true, ifeq(true, true, less_equal(idQa, divide(idQa, a)), true), true), true), true, ifeq2(less_equal(divide(idQa, a), idQa), true, divide(idQa, a), idQa), idQa)
% 39.05/5.48 = { by axiom 7 (ifeq_axiom_001) }
% 39.05/5.48 ifeq2(ifeq(quotient(idQa, a, divide(idQa, a)), true, ifeq(true, true, less_equal(idQa, divide(idQa, a)), true), true), true, ifeq2(less_equal(divide(idQa, a), idQa), true, divide(idQa, a), idQa), idQa)
% 39.05/5.48 = { by axiom 7 (ifeq_axiom_001) }
% 39.05/5.48 ifeq2(ifeq(quotient(idQa, a, divide(idQa, a)), true, less_equal(idQa, divide(idQa, a)), true), true, ifeq2(less_equal(divide(idQa, a), idQa), true, divide(idQa, a), idQa), idQa)
% 39.05/5.48 = { by axiom 9 (closure) }
% 39.05/5.48 ifeq2(ifeq(true, true, less_equal(idQa, divide(idQa, a)), true), true, ifeq2(less_equal(divide(idQa, a), idQa), true, divide(idQa, a), idQa), idQa)
% 39.05/5.48 = { by axiom 7 (ifeq_axiom_001) }
% 39.05/5.48 ifeq2(less_equal(idQa, divide(idQa, a)), true, ifeq2(less_equal(divide(idQa, a), idQa), true, divide(idQa, a), idQa), idQa)
% 39.05/5.48 = { by axiom 11 (less_equal_and_equal) }
% 39.05/5.48 idQa
% 39.05/5.48
% 39.05/5.48 Lemma 18: divide(idQa, idQ_idQa) = idQa_Q__idQ_idQa.
% 39.05/5.48 Proof:
% 39.05/5.48 divide(idQa, idQ_idQa)
% 39.05/5.48 = { by axiom 12 (well_defined) R->L }
% 39.05/5.48 ifeq2(quotient(idQa, idQ_idQa, divide(idQa, idQ_idQa)), true, ifeq2(quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa), true, idQa_Q__idQ_idQa, divide(idQa, idQ_idQa)), divide(idQa, idQ_idQa))
% 39.05/5.48 = { by axiom 6 (identity_divide_idQ_idQa) }
% 39.05/5.48 ifeq2(quotient(idQa, idQ_idQa, divide(idQa, idQ_idQa)), true, ifeq2(true, true, idQa_Q__idQ_idQa, divide(idQa, idQ_idQa)), divide(idQa, idQ_idQa))
% 39.05/5.48 = { by axiom 8 (ifeq_axiom) }
% 39.05/5.48 ifeq2(quotient(idQa, idQ_idQa, divide(idQa, idQ_idQa)), true, idQa_Q__idQ_idQa, divide(idQa, idQ_idQa))
% 39.05/5.48 = { by axiom 9 (closure) }
% 39.05/5.48 ifeq2(true, true, idQa_Q__idQ_idQa, divide(idQa, idQ_idQa))
% 39.05/5.48 = { by axiom 8 (ifeq_axiom) }
% 39.05/5.48 idQa_Q__idQ_idQa
% 39.05/5.48
% 39.05/5.48 Goal 1 (prove_idQa_equals_idQa_Q__idQ_idQa): idQa = idQa_Q__idQ_idQa.
% 39.05/5.48 Proof:
% 39.05/5.48 idQa
% 39.05/5.48 = { by lemma 17 R->L }
% 39.05/5.48 divide(idQa, a)
% 39.05/5.48 = { by axiom 11 (less_equal_and_equal) R->L }
% 39.05/5.48 ifeq2(less_equal(divide(idQa, a), divide(idQa, idQ_idQa)), true, ifeq2(less_equal(divide(idQa, idQ_idQa), divide(idQa, a)), true, divide(idQa, idQ_idQa), divide(idQa, a)), divide(idQa, a))
% 39.05/5.48 = { by axiom 7 (ifeq_axiom_001) R->L }
% 39.05/5.48 ifeq2(ifeq(true, true, less_equal(divide(idQa, a), divide(idQa, idQ_idQa)), true), true, ifeq2(less_equal(divide(idQa, idQ_idQa), divide(idQa, a)), true, divide(idQa, idQ_idQa), divide(idQa, a)), divide(idQa, a))
% 39.05/5.48 = { by axiom 14 (xQyLEz_implies_xQzLEy) R->L }
% 39.05/5.48 ifeq2(ifeq(ifeq(quotient(identity, idQa, idQ_idQa), true, ifeq(quotient(identity, a, idQa), true, ifeq(less_equal(idQa, idQa), true, less_equal(idQ_idQa, a), true), true), true), true, less_equal(divide(idQa, a), divide(idQa, idQ_idQa)), true), true, ifeq2(less_equal(divide(idQa, idQ_idQa), divide(idQa, a)), true, divide(idQa, idQ_idQa), divide(idQa, a)), divide(idQa, a))
% 39.05/5.48 = { by axiom 4 (identity_divide_idQa) }
% 39.05/5.48 ifeq2(ifeq(ifeq(true, true, ifeq(quotient(identity, a, idQa), true, ifeq(less_equal(idQa, idQa), true, less_equal(idQ_idQa, a), true), true), true), true, less_equal(divide(idQa, a), divide(idQa, idQ_idQa)), true), true, ifeq2(less_equal(divide(idQa, idQ_idQa), divide(idQa, a)), true, divide(idQa, idQ_idQa), divide(idQa, a)), divide(idQa, a))
% 39.05/5.48 = { by axiom 7 (ifeq_axiom_001) }
% 39.05/5.48 ifeq2(ifeq(ifeq(quotient(identity, a, idQa), true, ifeq(less_equal(idQa, idQa), true, less_equal(idQ_idQa, a), true), true), true, less_equal(divide(idQa, a), divide(idQa, idQ_idQa)), true), true, ifeq2(less_equal(divide(idQa, idQ_idQa), divide(idQa, a)), true, divide(idQa, idQ_idQa), divide(idQa, a)), divide(idQa, a))
% 39.05/5.48 = { by axiom 5 (identity_divide_a) }
% 39.05/5.48 ifeq2(ifeq(ifeq(true, true, ifeq(less_equal(idQa, idQa), true, less_equal(idQ_idQa, a), true), true), true, less_equal(divide(idQa, a), divide(idQa, idQ_idQa)), true), true, ifeq2(less_equal(divide(idQa, idQ_idQa), divide(idQa, a)), true, divide(idQa, idQ_idQa), divide(idQa, a)), divide(idQa, a))
% 39.05/5.48 = { by axiom 7 (ifeq_axiom_001) }
% 39.05/5.48 ifeq2(ifeq(ifeq(less_equal(idQa, idQa), true, less_equal(idQ_idQa, a), true), true, less_equal(divide(idQa, a), divide(idQa, idQ_idQa)), true), true, ifeq2(less_equal(divide(idQa, idQ_idQa), divide(idQa, a)), true, divide(idQa, idQ_idQa), divide(idQa, a)), divide(idQa, a))
% 39.05/5.48 = { by axiom 7 (ifeq_axiom_001) R->L }
% 39.05/5.48 ifeq2(ifeq(ifeq(ifeq(true, true, less_equal(idQa, idQa), true), true, less_equal(idQ_idQa, a), true), true, less_equal(divide(idQa, a), divide(idQa, idQ_idQa)), true), true, ifeq2(less_equal(divide(idQa, idQ_idQa), divide(idQa, a)), true, divide(idQa, idQ_idQa), divide(idQa, a)), divide(idQa, a))
% 39.05/5.48 = { by axiom 3 (x_divde_zero_is_x) R->L }
% 39.05/5.48 ifeq2(ifeq(ifeq(ifeq(quotient(idQa, zero, idQa), true, less_equal(idQa, idQa), true), true, less_equal(idQ_idQa, a), true), true, less_equal(divide(idQa, a), divide(idQa, idQ_idQa)), true), true, ifeq2(less_equal(divide(idQa, idQ_idQa), divide(idQa, a)), true, divide(idQa, idQ_idQa), divide(idQa, a)), divide(idQa, a))
% 39.05/5.48 = { by axiom 10 (divisor_existence) }
% 39.05/5.48 ifeq2(ifeq(ifeq(true, true, less_equal(idQ_idQa, a), true), true, less_equal(divide(idQa, a), divide(idQa, idQ_idQa)), true), true, ifeq2(less_equal(divide(idQa, idQ_idQa), divide(idQa, a)), true, divide(idQa, idQ_idQa), divide(idQa, a)), divide(idQa, a))
% 39.05/5.48 = { by axiom 7 (ifeq_axiom_001) }
% 39.05/5.48 ifeq2(ifeq(less_equal(idQ_idQa, a), true, less_equal(divide(idQa, a), divide(idQa, idQ_idQa)), true), true, ifeq2(less_equal(divide(idQa, idQ_idQa), divide(idQa, a)), true, divide(idQa, idQ_idQa), divide(idQa, a)), divide(idQa, a))
% 39.05/5.48 = { by axiom 7 (ifeq_axiom_001) R->L }
% 39.05/5.48 ifeq2(ifeq(true, true, ifeq(less_equal(idQ_idQa, a), true, less_equal(divide(idQa, a), divide(idQa, idQ_idQa)), true), true), true, ifeq2(less_equal(divide(idQa, idQ_idQa), divide(idQa, a)), true, divide(idQa, idQ_idQa), divide(idQa, a)), divide(idQa, a))
% 39.05/5.48 = { by axiom 9 (closure) R->L }
% 39.05/5.48 ifeq2(ifeq(quotient(idQa, idQ_idQa, divide(idQa, idQ_idQa)), true, ifeq(less_equal(idQ_idQa, a), true, less_equal(divide(idQa, a), divide(idQa, idQ_idQa)), true), true), true, ifeq2(less_equal(divide(idQa, idQ_idQa), divide(idQa, a)), true, divide(idQa, idQ_idQa), divide(idQa, a)), divide(idQa, a))
% 39.05/5.48 = { by axiom 7 (ifeq_axiom_001) R->L }
% 39.05/5.48 ifeq2(ifeq(true, true, ifeq(quotient(idQa, idQ_idQa, divide(idQa, idQ_idQa)), true, ifeq(less_equal(idQ_idQa, a), true, less_equal(divide(idQa, a), divide(idQa, idQ_idQa)), true), true), true), true, ifeq2(less_equal(divide(idQa, idQ_idQa), divide(idQa, a)), true, divide(idQa, idQ_idQa), divide(idQa, a)), divide(idQa, a))
% 39.05/5.48 = { by axiom 9 (closure) R->L }
% 39.05/5.48 ifeq2(ifeq(quotient(idQa, a, divide(idQa, a)), true, ifeq(quotient(idQa, idQ_idQa, divide(idQa, idQ_idQa)), true, ifeq(less_equal(idQ_idQa, a), true, less_equal(divide(idQa, a), divide(idQa, idQ_idQa)), true), true), true), true, ifeq2(less_equal(divide(idQa, idQ_idQa), divide(idQa, a)), true, divide(idQa, idQ_idQa), divide(idQa, a)), divide(idQa, a))
% 39.05/5.48 = { by axiom 13 (xLEy_implies_zQyLEzQx) }
% 39.05/5.48 ifeq2(true, true, ifeq2(less_equal(divide(idQa, idQ_idQa), divide(idQa, a)), true, divide(idQa, idQ_idQa), divide(idQa, a)), divide(idQa, a))
% 39.05/5.48 = { by axiom 8 (ifeq_axiom) }
% 39.05/5.48 ifeq2(less_equal(divide(idQa, idQ_idQa), divide(idQa, a)), true, divide(idQa, idQ_idQa), divide(idQa, a))
% 39.05/5.48 = { by lemma 18 }
% 39.05/5.48 ifeq2(less_equal(idQa_Q__idQ_idQa, divide(idQa, a)), true, divide(idQa, idQ_idQa), divide(idQa, a))
% 39.05/5.48 = { by lemma 17 }
% 39.05/5.48 ifeq2(less_equal(idQa_Q__idQ_idQa, divide(idQa, a)), true, divide(idQa, idQ_idQa), idQa)
% 39.05/5.48 = { by lemma 17 }
% 39.05/5.48 ifeq2(less_equal(idQa_Q__idQ_idQa, idQa), true, divide(idQa, idQ_idQa), idQa)
% 39.05/5.48 = { by axiom 7 (ifeq_axiom_001) R->L }
% 39.05/5.48 ifeq2(ifeq(true, true, less_equal(idQa_Q__idQ_idQa, idQa), true), true, divide(idQa, idQ_idQa), idQa)
% 39.05/5.48 = { by axiom 6 (identity_divide_idQ_idQa) R->L }
% 39.05/5.48 ifeq2(ifeq(quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa), true, less_equal(idQa_Q__idQ_idQa, idQa), true), true, divide(idQa, idQ_idQa), idQa)
% 39.05/5.48 = { by axiom 10 (divisor_existence) }
% 39.05/5.48 ifeq2(true, true, divide(idQa, idQ_idQa), idQa)
% 39.05/5.48 = { by axiom 8 (ifeq_axiom) }
% 39.05/5.48 divide(idQa, idQ_idQa)
% 39.05/5.48 = { by lemma 18 }
% 39.05/5.48 idQa_Q__idQ_idQa
% 39.05/5.48 % SZS output end Proof
% 39.05/5.48
% 39.05/5.48 RESULT: Unsatisfiable (the axioms are contradictory).
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