TSTP Solution File: LCL899+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL899+1 : TPTP v8.1.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.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 : 600s
% DateTime : Sun Jul 17 12:56:50 EDT 2022
% Result : Theorem 1.37s 1.57s
% Output : CNFRefutation 1.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL899+1 : TPTP v8.1.0. Released v5.5.0.
% 0.00/0.12 % Command : metis --show proof --show saturation %s
% 0.11/0.33 % Computer : n015.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sun Jul 3 17:16:45 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.37/1.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.37/1.57
% 1.37/1.57 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.37/1.57 fof(sos_02, axiom, (! [A, B] : add(A, B) = add(B, A))).
% 1.37/1.57
% 1.37/1.57 fof(sos_03, axiom, (! [A] : add(A, 0) = A)).
% 1.37/1.57
% 1.37/1.57 fof(sos_04, axiom, (! [A] : greater_equal(A, A))).
% 1.37/1.57
% 1.37/1.57 fof(sos_06, axiom,
% 1.37/1.57 (! [X3, X4] :
% 1.37/1.57 ((greater_equal(X3, X4) & greater_equal(X4, X3)) => X3 = X4))).
% 1.37/1.57
% 1.37/1.57 fof(sos_07, axiom,
% 1.37/1.57 (! [X5, X6, X7] :
% 1.37/1.57 (greater_equal(add(X5, X6), X7) <=>
% 1.37/1.57 greater_equal(X6, '==>'(X5, X7))))).
% 1.37/1.57
% 1.37/1.57 fof(sos_08, axiom, (! [A] : greater_equal(A, 0))).
% 1.37/1.57
% 1.37/1.57 fof(sos_09, axiom,
% 1.37/1.57 (! [X8, X9, X10] :
% 1.37/1.57 (greater_equal(X8, X9) =>
% 1.37/1.57 greater_equal(add(X8, X10), add(X9, X10))))).
% 1.37/1.57
% 1.37/1.57 fof(sos_12, axiom, (! [A] : add(A, 1) = 1)).
% 1.37/1.57
% 1.37/1.57 fof(sos_13, axiom,
% 1.37/1.57 (! [A, B] : '==>'('==>'(A, B), B) = '==>'('==>'(B, A), A))).
% 1.37/1.57
% 1.37/1.57 fof(goals_14, conjecture, (! [X17] : '==>'('==>'(X17, 1), 1) = X17)).
% 1.37/1.57
% 1.37/1.57 fof(subgoal_0, plain, (! [X17] : '==>'('==>'(X17, 1), 1) = X17),
% 1.37/1.57 inference(strip, [], [goals_14])).
% 1.37/1.57
% 1.37/1.57 fof(negate_0_0, plain, (~ ! [X17] : '==>'('==>'(X17, 1), 1) = X17),
% 1.37/1.57 inference(negate, [], [subgoal_0])).
% 1.37/1.57
% 1.37/1.57 fof(normalize_0_0, plain, (? [X17] : '==>'('==>'(X17, 1), 1) != X17),
% 1.37/1.57 inference(canonicalize, [], [negate_0_0])).
% 1.37/1.57
% 1.37/1.57 fof(normalize_0_1, plain,
% 1.37/1.57 ('==>'('==>'(skolemFOFtoCNF_X17, 1), 1) != skolemFOFtoCNF_X17),
% 1.37/1.57 inference(skolemize, [], [normalize_0_0])).
% 1.37/1.57
% 1.37/1.57 fof(normalize_0_2, plain,
% 1.37/1.57 (! [A, B] : '==>'('==>'(A, B), B) = '==>'('==>'(B, A), A)),
% 1.37/1.57 inference(canonicalize, [], [sos_13])).
% 1.37/1.57
% 1.37/1.57 fof(normalize_0_3, plain,
% 1.37/1.57 (! [A, B] : '==>'('==>'(A, B), B) = '==>'('==>'(B, A), A)),
% 1.37/1.57 inference(specialize, [], [normalize_0_2])).
% 1.37/1.57
% 1.37/1.57 fof(normalize_0_4, plain, (! [A] : greater_equal(A, A)),
% 1.37/1.57 inference(canonicalize, [], [sos_04])).
% 1.37/1.57
% 1.37/1.57 fof(normalize_0_5, plain, (! [A] : greater_equal(A, A)),
% 1.37/1.57 inference(specialize, [], [normalize_0_4])).
% 1.37/1.57
% 1.37/1.57 fof(normalize_0_6, plain,
% 1.37/1.57 (! [X5, X6, X7] :
% 1.37/1.57 (~ greater_equal(X6, '==>'(X5, X7)) <=>
% 1.37/1.57 ~ greater_equal(add(X5, X6), X7))),
% 1.37/1.57 inference(canonicalize, [], [sos_07])).
% 1.37/1.57
% 1.37/1.57 fof(normalize_0_7, plain,
% 1.37/1.57 (! [X5, X6, X7] :
% 1.37/1.57 (~ greater_equal(X6, '==>'(X5, X7)) <=>
% 1.37/1.57 ~ greater_equal(add(X5, X6), X7))),
% 1.37/1.57 inference(specialize, [], [normalize_0_6])).
% 1.37/1.57
% 1.37/1.57 fof(normalize_0_8, plain,
% 1.37/1.57 (! [X5, X6, X7] :
% 1.37/1.57 ((~ greater_equal(X6, '==>'(X5, X7)) |
% 1.37/1.57 greater_equal(add(X5, X6), X7)) &
% 1.37/1.57 (~ greater_equal(add(X5, X6), X7) |
% 1.37/1.57 greater_equal(X6, '==>'(X5, X7))))),
% 1.37/1.57 inference(clausify, [], [normalize_0_7])).
% 1.37/1.57
% 1.37/1.57 fof(normalize_0_9, plain,
% 1.37/1.57 (! [X5, X6, X7] :
% 1.37/1.57 (~ greater_equal(X6, '==>'(X5, X7)) |
% 1.37/1.57 greater_equal(add(X5, X6), X7))),
% 1.37/1.57 inference(conjunct, [], [normalize_0_8])).
% 1.37/1.57
% 1.37/1.57 fof(normalize_0_10, plain, (! [A] : add(A, 0) = A),
% 1.37/1.57 inference(canonicalize, [], [sos_03])).
% 1.37/1.57
% 1.37/1.57 fof(normalize_0_11, plain, (! [A] : add(A, 0) = A),
% 1.37/1.57 inference(specialize, [], [normalize_0_10])).
% 1.37/1.57
% 1.37/1.57 fof(normalize_0_12, plain, (! [A, B] : add(A, B) = add(B, A)),
% 1.37/1.57 inference(canonicalize, [], [sos_02])).
% 1.37/1.57
% 1.37/1.57 fof(normalize_0_13, plain, (! [A, B] : add(A, B) = add(B, A)),
% 1.37/1.57 inference(specialize, [], [normalize_0_12])).
% 1.37/1.57
% 1.37/1.57 fof(normalize_0_14, plain,
% 1.37/1.57 (! [X3, X4] :
% 1.37/1.57 (~ greater_equal(X3, X4) | ~ greater_equal(X4, X3) | X3 = X4)),
% 1.37/1.57 inference(canonicalize, [], [sos_06])).
% 1.37/1.57
% 1.37/1.57 fof(normalize_0_15, plain,
% 1.37/1.57 (! [X3, X4] :
% 1.37/1.57 (~ greater_equal(X3, X4) | ~ greater_equal(X4, X3) | X3 = X4)),
% 1.37/1.57 inference(specialize, [], [normalize_0_14])).
% 1.37/1.57
% 1.37/1.57 fof(normalize_0_16, plain, (! [A] : greater_equal(A, 0)),
% 1.37/1.57 inference(canonicalize, [], [sos_08])).
% 1.37/1.57
% 1.37/1.57 fof(normalize_0_17, plain, (! [A] : greater_equal(A, 0)),
% 1.37/1.57 inference(specialize, [], [normalize_0_16])).
% 1.37/1.57
% 1.37/1.57 fof(normalize_0_18, plain,
% 1.37/1.57 (! [X8, X9] :
% 1.37/1.57 (~ greater_equal(X8, X9) |
% 1.37/1.57 ! [X10] : greater_equal(add(X8, X10), add(X9, X10)))),
% 1.37/1.57 inference(canonicalize, [], [sos_09])).
% 1.37/1.57
% 1.37/1.57 fof(normalize_0_19, plain,
% 1.37/1.57 (! [X8, X9] :
% 1.37/1.57 (~ greater_equal(X8, X9) |
% 1.37/1.57 ! [X10] : greater_equal(add(X8, X10), add(X9, X10)))),
% 1.37/1.57 inference(specialize, [], [normalize_0_18])).
% 1.37/1.57
% 1.37/1.57 fof(normalize_0_20, plain,
% 1.37/1.57 (! [X10, X8, X9] :
% 1.37/1.57 (~ greater_equal(X8, X9) |
% 1.37/1.57 greater_equal(add(X8, X10), add(X9, X10)))),
% 1.37/1.57 inference(clausify, [], [normalize_0_19])).
% 1.37/1.57
% 1.37/1.57 fof(normalize_0_21, plain,
% 1.37/1.57 (! [X5, X6, X7] :
% 1.37/1.57 (~ greater_equal(add(X5, X6), X7) |
% 1.37/1.57 greater_equal(X6, '==>'(X5, X7)))),
% 1.37/1.57 inference(conjunct, [], [normalize_0_8])).
% 1.37/1.57
% 1.37/1.57 fof(normalize_0_22, plain, (! [A] : add(A, 1) = 1),
% 1.37/1.57 inference(canonicalize, [], [sos_12])).
% 1.37/1.57
% 1.37/1.57 fof(normalize_0_23, plain, (! [A] : add(A, 1) = 1),
% 1.37/1.57 inference(specialize, [], [normalize_0_22])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_0, plain,
% 1.37/1.57 ('==>'('==>'(skolemFOFtoCNF_X17, 1), 1) != skolemFOFtoCNF_X17),
% 1.37/1.57 inference(canonicalize, [], [normalize_0_1])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_1, plain, ('==>'('==>'(A, B), B) = '==>'('==>'(B, A), A)),
% 1.37/1.57 inference(canonicalize, [], [normalize_0_3])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_2, plain, (X = X), introduced(tautology, [refl, [$fot(X)]])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_3, plain, (X != X | X != Y | Y = X),
% 1.37/1.57 introduced(tautology, [equality, [$cnf($equal(X, X)), [0], $fot(Y)]])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_4, plain, (X != Y | Y = X),
% 1.37/1.57 inference(resolve, [$cnf($equal(X, X))], [refute_0_2, refute_0_3])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_5, plain,
% 1.37/1.57 ('==>'('==>'(A, B), B) != '==>'('==>'(B, A), A) |
% 1.37/1.57 '==>'('==>'(B, A), A) = '==>'('==>'(A, B), B)),
% 1.37/1.57 inference(subst, [],
% 1.37/1.57 [refute_0_4 :
% 1.37/1.57 [bind(X, $fot('==>'('==>'(A, B), B))),
% 1.37/1.57 bind(Y, $fot('==>'('==>'(B, A), A)))]])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_6, plain, ('==>'('==>'(B, A), A) = '==>'('==>'(A, B), B)),
% 1.37/1.57 inference(resolve,
% 1.37/1.57 [$cnf($equal('==>'('==>'(A, B), B), '==>'('==>'(B, A), A)))],
% 1.37/1.57 [refute_0_1, refute_0_5])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_7, plain,
% 1.37/1.57 ('==>'('==>'(skolemFOFtoCNF_X17, 1), 1) =
% 1.37/1.57 '==>'('==>'(1, skolemFOFtoCNF_X17), skolemFOFtoCNF_X17)),
% 1.37/1.57 inference(subst, [],
% 1.37/1.57 [refute_0_6 :
% 1.37/1.57 [bind(A, $fot(1)), bind(B, $fot(skolemFOFtoCNF_X17))]])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_8, plain,
% 1.37/1.57 ('==>'('==>'(1, skolemFOFtoCNF_X17), skolemFOFtoCNF_X17) !=
% 1.37/1.57 skolemFOFtoCNF_X17 |
% 1.37/1.57 '==>'('==>'(skolemFOFtoCNF_X17, 1), 1) !=
% 1.37/1.57 '==>'('==>'(1, skolemFOFtoCNF_X17), skolemFOFtoCNF_X17) |
% 1.37/1.57 '==>'('==>'(skolemFOFtoCNF_X17, 1), 1) = skolemFOFtoCNF_X17),
% 1.37/1.57 introduced(tautology,
% 1.37/1.57 [equality,
% 1.37/1.57 [$cnf($equal('==>'('==>'(skolemFOFtoCNF_X17, 1), 1),
% 1.37/1.57 '==>'('==>'(1, skolemFOFtoCNF_X17),
% 1.37/1.57 skolemFOFtoCNF_X17))), [1],
% 1.37/1.57 $fot(skolemFOFtoCNF_X17)]])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_9, plain,
% 1.37/1.57 ('==>'('==>'(1, skolemFOFtoCNF_X17), skolemFOFtoCNF_X17) !=
% 1.37/1.57 skolemFOFtoCNF_X17 |
% 1.37/1.57 '==>'('==>'(skolemFOFtoCNF_X17, 1), 1) = skolemFOFtoCNF_X17),
% 1.37/1.57 inference(resolve,
% 1.37/1.57 [$cnf($equal('==>'('==>'(skolemFOFtoCNF_X17, 1), 1),
% 1.37/1.57 '==>'('==>'(1, skolemFOFtoCNF_X17),
% 1.37/1.57 skolemFOFtoCNF_X17)))], [refute_0_7, refute_0_8])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_10, plain,
% 1.37/1.57 ('==>'('==>'(1, skolemFOFtoCNF_X17), skolemFOFtoCNF_X17) !=
% 1.37/1.57 skolemFOFtoCNF_X17),
% 1.37/1.57 inference(resolve,
% 1.37/1.57 [$cnf($equal('==>'('==>'(skolemFOFtoCNF_X17, 1), 1),
% 1.37/1.57 skolemFOFtoCNF_X17))], [refute_0_9, refute_0_0])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_11, plain, (greater_equal(A, A)),
% 1.37/1.57 inference(canonicalize, [], [normalize_0_5])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_12, plain,
% 1.37/1.57 (greater_equal('==>'(X_79, X_81), '==>'(X_79, X_81))),
% 1.37/1.57 inference(subst, [],
% 1.37/1.57 [refute_0_11 : [bind(A, $fot('==>'(X_79, X_81)))]])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_13, plain,
% 1.37/1.57 (~ greater_equal(X6, '==>'(X5, X7)) | greater_equal(add(X5, X6), X7)),
% 1.37/1.57 inference(canonicalize, [], [normalize_0_9])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_14, plain,
% 1.37/1.57 (~ greater_equal('==>'(X_79, X_81), '==>'(X_79, X_81)) |
% 1.37/1.57 greater_equal(add(X_79, '==>'(X_79, X_81)), X_81)),
% 1.37/1.57 inference(subst, [],
% 1.37/1.57 [refute_0_13 :
% 1.37/1.57 [bind(X5, $fot(X_79)), bind(X6, $fot('==>'(X_79, X_81))),
% 1.37/1.57 bind(X7, $fot(X_81))]])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_15, plain,
% 1.37/1.57 (greater_equal(add(X_79, '==>'(X_79, X_81)), X_81)),
% 1.37/1.57 inference(resolve,
% 1.37/1.57 [$cnf(greater_equal('==>'(X_79, X_81), '==>'(X_79, X_81)))],
% 1.37/1.57 [refute_0_12, refute_0_14])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_16, plain, (greater_equal(add(0, '==>'(0, X_83)), X_83)),
% 1.37/1.57 inference(subst, [],
% 1.37/1.57 [refute_0_15 :
% 1.37/1.57 [bind(X_79, $fot(0)), bind(X_81, $fot(X_83))]])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_17, plain, (add(A, 0) = A),
% 1.37/1.57 inference(canonicalize, [], [normalize_0_11])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_18, plain, (add(A, B) = add(B, A)),
% 1.37/1.57 inference(canonicalize, [], [normalize_0_13])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_19, plain, (add(A, 0) = add(0, A)),
% 1.37/1.57 inference(subst, [], [refute_0_18 : [bind(B, $fot(0))]])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_20, plain,
% 1.37/1.57 (add(A, 0) != A | add(A, 0) != add(0, A) | add(0, A) = A),
% 1.37/1.57 introduced(tautology,
% 1.37/1.57 [equality,
% 1.37/1.57 [$cnf($equal(add(A, 0), A)), [0], $fot(add(0, A))]])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_21, plain, (add(A, 0) != A | add(0, A) = A),
% 1.37/1.57 inference(resolve, [$cnf($equal(add(A, 0), add(0, A)))],
% 1.37/1.57 [refute_0_19, refute_0_20])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_22, plain, (add(0, A) = A),
% 1.37/1.57 inference(resolve, [$cnf($equal(add(A, 0), A))],
% 1.37/1.57 [refute_0_17, refute_0_21])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_23, plain, (add(0, '==>'(0, X_83)) = '==>'(0, X_83)),
% 1.37/1.57 inference(subst, [], [refute_0_22 : [bind(A, $fot('==>'(0, X_83)))]])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_24, plain,
% 1.37/1.57 (add(0, '==>'(0, X_83)) != '==>'(0, X_83) |
% 1.37/1.57 ~ greater_equal(add(0, '==>'(0, X_83)), X_83) |
% 1.37/1.57 greater_equal('==>'(0, X_83), X_83)),
% 1.37/1.57 introduced(tautology,
% 1.37/1.57 [equality,
% 1.37/1.57 [$cnf(greater_equal(add(0, '==>'(0, X_83)), X_83)), [0],
% 1.37/1.57 $fot('==>'(0, X_83))]])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_25, plain,
% 1.37/1.57 (~ greater_equal(add(0, '==>'(0, X_83)), X_83) |
% 1.37/1.57 greater_equal('==>'(0, X_83), X_83)),
% 1.37/1.57 inference(resolve,
% 1.37/1.57 [$cnf($equal(add(0, '==>'(0, X_83)), '==>'(0, X_83)))],
% 1.37/1.57 [refute_0_23, refute_0_24])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_26, plain, (greater_equal('==>'(0, X_83), X_83)),
% 1.37/1.57 inference(resolve, [$cnf(greater_equal(add(0, '==>'(0, X_83)), X_83))],
% 1.37/1.57 [refute_0_16, refute_0_25])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_27, plain, (greater_equal('==>'(0, X_344), X_344)),
% 1.37/1.57 inference(subst, [], [refute_0_26 : [bind(X_83, $fot(X_344))]])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_28, plain,
% 1.37/1.57 (~ greater_equal(X3, X4) | ~ greater_equal(X4, X3) | X3 = X4),
% 1.37/1.57 inference(canonicalize, [], [normalize_0_15])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_29, plain,
% 1.37/1.57 (~ greater_equal(X_344, '==>'(0, X_344)) |
% 1.37/1.57 ~ greater_equal('==>'(0, X_344), X_344) | '==>'(0, X_344) = X_344),
% 1.37/1.57 inference(subst, [],
% 1.37/1.57 [refute_0_28 :
% 1.37/1.57 [bind(X3, $fot('==>'(0, X_344))), bind(X4, $fot(X_344))]])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_30, plain,
% 1.37/1.57 (~ greater_equal(X_344, '==>'(0, X_344)) | '==>'(0, X_344) = X_344),
% 1.37/1.57 inference(resolve, [$cnf(greater_equal('==>'(0, X_344), X_344))],
% 1.37/1.57 [refute_0_27, refute_0_29])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_31, plain, (greater_equal(A, 0)),
% 1.37/1.57 inference(canonicalize, [], [normalize_0_17])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_32, plain, (greater_equal(X_25, 0)),
% 1.37/1.57 inference(subst, [], [refute_0_31 : [bind(A, $fot(X_25))]])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_33, plain,
% 1.37/1.57 (~ greater_equal(X8, X9) | greater_equal(add(X8, X10), add(X9, X10))),
% 1.37/1.57 inference(canonicalize, [], [normalize_0_20])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_34, plain,
% 1.37/1.57 (~ greater_equal(X_25, 0) |
% 1.37/1.57 greater_equal(add(X_25, X_24), add(0, X_24))),
% 1.37/1.57 inference(subst, [],
% 1.37/1.57 [refute_0_33 :
% 1.37/1.57 [bind(X10, $fot(X_24)), bind(X8, $fot(X_25)),
% 1.37/1.57 bind(X9, $fot(0))]])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_35, plain, (greater_equal(add(X_25, X_24), add(0, X_24))),
% 1.37/1.57 inference(resolve, [$cnf(greater_equal(X_25, 0))],
% 1.37/1.57 [refute_0_32, refute_0_34])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_36, plain, (add(0, X_24) = X_24),
% 1.37/1.57 inference(subst, [], [refute_0_22 : [bind(A, $fot(X_24))]])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_37, plain,
% 1.37/1.57 (add(0, X_24) != X_24 |
% 1.37/1.57 ~ greater_equal(add(X_25, X_24), add(0, X_24)) |
% 1.37/1.57 greater_equal(add(X_25, X_24), X_24)),
% 1.37/1.57 introduced(tautology,
% 1.37/1.57 [equality,
% 1.37/1.57 [$cnf(greater_equal(add(X_25, X_24), add(0, X_24))), [1],
% 1.37/1.57 $fot(X_24)]])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_38, plain,
% 1.37/1.57 (~ greater_equal(add(X_25, X_24), add(0, X_24)) |
% 1.37/1.57 greater_equal(add(X_25, X_24), X_24)),
% 1.37/1.57 inference(resolve, [$cnf($equal(add(0, X_24), X_24))],
% 1.37/1.57 [refute_0_36, refute_0_37])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_39, plain, (greater_equal(add(X_25, X_24), X_24)),
% 1.37/1.57 inference(resolve,
% 1.37/1.57 [$cnf(greater_equal(add(X_25, X_24), add(0, X_24)))],
% 1.37/1.57 [refute_0_35, refute_0_38])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_40, plain, (greater_equal(add(X_123, X_125), X_125)),
% 1.37/1.57 inference(subst, [],
% 1.37/1.57 [refute_0_39 :
% 1.37/1.57 [bind(X_24, $fot(X_125)), bind(X_25, $fot(X_123))]])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_41, plain,
% 1.37/1.57 (~ greater_equal(add(X5, X6), X7) | greater_equal(X6, '==>'(X5, X7))),
% 1.37/1.57 inference(canonicalize, [], [normalize_0_21])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_42, plain,
% 1.37/1.57 (~ greater_equal(add(X_123, X_125), X_125) |
% 1.37/1.57 greater_equal(X_125, '==>'(X_123, X_125))),
% 1.37/1.57 inference(subst, [],
% 1.37/1.57 [refute_0_41 :
% 1.37/1.57 [bind(X5, $fot(X_123)), bind(X6, $fot(X_125)),
% 1.37/1.57 bind(X7, $fot(X_125))]])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_43, plain, (greater_equal(X_125, '==>'(X_123, X_125))),
% 1.37/1.57 inference(resolve, [$cnf(greater_equal(add(X_123, X_125), X_125))],
% 1.37/1.57 [refute_0_40, refute_0_42])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_44, plain, (greater_equal(X_344, '==>'(0, X_344))),
% 1.37/1.57 inference(subst, [],
% 1.37/1.57 [refute_0_43 :
% 1.37/1.57 [bind(X_123, $fot(0)), bind(X_125, $fot(X_344))]])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_45, plain, ('==>'(0, X_344) = X_344),
% 1.37/1.57 inference(resolve, [$cnf(greater_equal(X_344, '==>'(0, X_344)))],
% 1.37/1.57 [refute_0_44, refute_0_30])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_46, plain,
% 1.37/1.57 ('==>'(0, skolemFOFtoCNF_X17) = skolemFOFtoCNF_X17),
% 1.37/1.57 inference(subst, [],
% 1.37/1.57 [refute_0_45 : [bind(X_344, $fot(skolemFOFtoCNF_X17))]])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_47, plain,
% 1.37/1.57 (~ greater_equal(X_136, '==>'(1, X_137)) |
% 1.37/1.57 greater_equal(add(X_136, X10), add('==>'(1, X_137), X10))),
% 1.37/1.57 inference(subst, [],
% 1.37/1.57 [refute_0_33 :
% 1.37/1.57 [bind(X8, $fot(X_136)), bind(X9, $fot('==>'(1, X_137)))]])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_48, plain,
% 1.37/1.57 (~ greater_equal(add(1, X_124), X_125) |
% 1.37/1.57 greater_equal(X_124, '==>'(1, X_125))),
% 1.37/1.57 inference(subst, [],
% 1.37/1.57 [refute_0_41 :
% 1.37/1.57 [bind(X5, $fot(1)), bind(X6, $fot(X_124)),
% 1.37/1.57 bind(X7, $fot(X_125))]])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_49, plain, (add(A, 1) = 1),
% 1.37/1.57 inference(canonicalize, [], [normalize_0_23])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_50, plain, (add(A, 1) = add(1, A)),
% 1.37/1.57 inference(subst, [], [refute_0_18 : [bind(B, $fot(1))]])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_51, plain,
% 1.37/1.57 (add(A, 1) != add(1, A) | add(A, 1) != 1 | add(1, A) = 1),
% 1.37/1.57 introduced(tautology,
% 1.37/1.57 [equality,
% 1.37/1.57 [$cnf($equal(add(A, 1), 1)), [0], $fot(add(1, A))]])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_52, plain, (add(A, 1) != 1 | add(1, A) = 1),
% 1.37/1.57 inference(resolve, [$cnf($equal(add(A, 1), add(1, A)))],
% 1.37/1.57 [refute_0_50, refute_0_51])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_53, plain, (add(1, A) = 1),
% 1.37/1.57 inference(resolve, [$cnf($equal(add(A, 1), 1))],
% 1.37/1.57 [refute_0_49, refute_0_52])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_54, plain, (add(1, X_124) = 1),
% 1.37/1.57 inference(subst, [], [refute_0_53 : [bind(A, $fot(X_124))]])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_55, plain,
% 1.37/1.57 (add(1, X_124) != 1 | ~ greater_equal(1, X_125) |
% 1.37/1.57 greater_equal(add(1, X_124), X_125)),
% 1.37/1.57 introduced(tautology,
% 1.37/1.57 [equality,
% 1.37/1.57 [$cnf(~ greater_equal(add(1, X_124), X_125)), [0],
% 1.37/1.57 $fot(1)]])).
% 1.37/1.57
% 1.37/1.57 cnf(refute_0_56, plain,
% 1.37/1.57 (~ greater_equal(1, X_125) | greater_equal(add(1, X_124), X_125)),
% 1.37/1.58 inference(resolve, [$cnf($equal(add(1, X_124), 1))],
% 1.37/1.58 [refute_0_54, refute_0_55])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_57, plain,
% 1.37/1.58 (~ greater_equal(1, X_125) | greater_equal(X_124, '==>'(1, X_125))),
% 1.37/1.58 inference(resolve, [$cnf(greater_equal(add(1, X_124), X_125))],
% 1.37/1.58 [refute_0_56, refute_0_48])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_58, plain, (greater_equal(add(1, X_27), X_27)),
% 1.37/1.58 inference(subst, [],
% 1.37/1.58 [refute_0_39 :
% 1.37/1.58 [bind(X_24, $fot(X_27)), bind(X_25, $fot(1))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_59, plain, (add(1, X_27) = 1),
% 1.37/1.58 inference(subst, [], [refute_0_53 : [bind(A, $fot(X_27))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_60, plain,
% 1.37/1.58 (add(1, X_27) != 1 | ~ greater_equal(add(1, X_27), X_27) |
% 1.37/1.58 greater_equal(1, X_27)),
% 1.37/1.58 introduced(tautology,
% 1.37/1.58 [equality,
% 1.37/1.58 [$cnf(greater_equal(add(1, X_27), X_27)), [0], $fot(1)]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_61, plain,
% 1.37/1.58 (~ greater_equal(add(1, X_27), X_27) | greater_equal(1, X_27)),
% 1.37/1.58 inference(resolve, [$cnf($equal(add(1, X_27), 1))],
% 1.37/1.58 [refute_0_59, refute_0_60])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_62, plain, (greater_equal(1, X_27)),
% 1.37/1.58 inference(resolve, [$cnf(greater_equal(add(1, X_27), X_27))],
% 1.37/1.58 [refute_0_58, refute_0_61])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_63, plain, (greater_equal(1, X_125)),
% 1.37/1.58 inference(subst, [], [refute_0_62 : [bind(X_27, $fot(X_125))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_64, plain, (greater_equal(X_124, '==>'(1, X_125))),
% 1.37/1.58 inference(resolve, [$cnf(greater_equal(1, X_125))],
% 1.37/1.58 [refute_0_63, refute_0_57])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_65, plain, (greater_equal(X_136, '==>'(1, X_137))),
% 1.37/1.58 inference(subst, [],
% 1.37/1.58 [refute_0_64 :
% 1.37/1.58 [bind(X_124, $fot(X_136)), bind(X_125, $fot(X_137))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_66, plain,
% 1.37/1.58 (greater_equal(add(X_136, X10), add('==>'(1, X_137), X10))),
% 1.37/1.58 inference(resolve, [$cnf(greater_equal(X_136, '==>'(1, X_137)))],
% 1.37/1.58 [refute_0_65, refute_0_47])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_67, plain,
% 1.37/1.58 (greater_equal(add(0, X_225), add('==>'(1, X_227), X_225))),
% 1.37/1.58 inference(subst, [],
% 1.37/1.58 [refute_0_66 :
% 1.37/1.58 [bind(X10, $fot(X_225)), bind(X_136, $fot(0)),
% 1.37/1.58 bind(X_137, $fot(X_227))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_68, plain, (add(0, X_225) = X_225),
% 1.37/1.58 inference(subst, [], [refute_0_22 : [bind(A, $fot(X_225))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_69, plain,
% 1.37/1.58 (add(0, X_225) != X_225 |
% 1.37/1.58 ~ greater_equal(add(0, X_225), add('==>'(1, X_227), X_225)) |
% 1.37/1.58 greater_equal(X_225, add('==>'(1, X_227), X_225))),
% 1.37/1.58 introduced(tautology,
% 1.37/1.58 [equality,
% 1.37/1.58 [$cnf(greater_equal(add(0, X_225),
% 1.37/1.58 add('==>'(1, X_227), X_225))), [0],
% 1.37/1.58 $fot(X_225)]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_70, plain,
% 1.37/1.58 (~ greater_equal(add(0, X_225), add('==>'(1, X_227), X_225)) |
% 1.37/1.58 greater_equal(X_225, add('==>'(1, X_227), X_225))),
% 1.37/1.58 inference(resolve, [$cnf($equal(add(0, X_225), X_225))],
% 1.37/1.58 [refute_0_68, refute_0_69])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_71, plain,
% 1.37/1.58 (greater_equal(X_225, add('==>'(1, X_227), X_225))),
% 1.37/1.58 inference(resolve,
% 1.37/1.58 [$cnf(greater_equal(add(0, X_225),
% 1.37/1.58 add('==>'(1, X_227), X_225)))],
% 1.37/1.58 [refute_0_67, refute_0_70])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_72, plain, (greater_equal(0, add('==>'(1, X_227), 0))),
% 1.37/1.58 inference(subst, [], [refute_0_71 : [bind(X_225, $fot(0))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_73, plain, (greater_equal(X_343, 0)),
% 1.37/1.58 inference(subst, [], [refute_0_31 : [bind(A, $fot(X_343))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_74, plain,
% 1.37/1.58 (~ greater_equal(X_343, 0) | ~ greater_equal(0, X_343) | X_343 = 0),
% 1.37/1.58 inference(subst, [],
% 1.37/1.58 [refute_0_28 : [bind(X3, $fot(X_343)), bind(X4, $fot(0))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_75, plain, (~ greater_equal(0, X_343) | X_343 = 0),
% 1.37/1.58 inference(resolve, [$cnf(greater_equal(X_343, 0))],
% 1.37/1.58 [refute_0_73, refute_0_74])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_76, plain,
% 1.37/1.58 (~ greater_equal(0, add('==>'(1, X_227), 0)) |
% 1.37/1.58 add('==>'(1, X_227), 0) = 0),
% 1.37/1.58 inference(subst, [],
% 1.37/1.58 [refute_0_75 :
% 1.37/1.58 [bind(X_343, $fot(add('==>'(1, X_227), 0)))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_77, plain, (add('==>'(1, X_227), 0) = 0),
% 1.37/1.58 inference(resolve, [$cnf(greater_equal(0, add('==>'(1, X_227), 0)))],
% 1.37/1.58 [refute_0_72, refute_0_76])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_78, plain, (add(0, '==>'(1, X_227)) = '==>'(1, X_227)),
% 1.37/1.58 inference(subst, [],
% 1.37/1.58 [refute_0_22 : [bind(A, $fot('==>'(1, X_227)))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_79, plain,
% 1.37/1.58 (~ greater_equal('==>'(0, X_84), X_84) |
% 1.37/1.58 greater_equal(add('==>'(0, X_84), X10), add(X_84, X10))),
% 1.37/1.58 inference(subst, [],
% 1.37/1.58 [refute_0_33 :
% 1.37/1.58 [bind(X8, $fot('==>'(0, X_84))), bind(X9, $fot(X_84))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_80, plain, (greater_equal('==>'(0, X_84), X_84)),
% 1.37/1.58 inference(subst, [], [refute_0_26 : [bind(X_83, $fot(X_84))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_81, plain,
% 1.37/1.58 (greater_equal(add('==>'(0, X_84), X10), add(X_84, X10))),
% 1.37/1.58 inference(resolve, [$cnf(greater_equal('==>'(0, X_84), X_84))],
% 1.37/1.58 [refute_0_80, refute_0_79])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_82, plain,
% 1.37/1.58 (greater_equal(add('==>'(0, X_116), X_115), add(X_116, X_115))),
% 1.37/1.58 inference(subst, [],
% 1.37/1.58 [refute_0_81 :
% 1.37/1.58 [bind(X10, $fot(X_115)), bind(X_84, $fot(X_116))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_83, plain,
% 1.37/1.58 (add(X_115, '==>'(0, X_116)) = add('==>'(0, X_116), X_115)),
% 1.37/1.58 inference(subst, [],
% 1.37/1.58 [refute_0_18 :
% 1.37/1.58 [bind(A, $fot(X_115)), bind(B, $fot('==>'(0, X_116)))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_84, plain,
% 1.37/1.58 (add(X_115, '==>'(0, X_116)) != add('==>'(0, X_116), X_115) |
% 1.37/1.58 add('==>'(0, X_116), X_115) = add(X_115, '==>'(0, X_116))),
% 1.37/1.58 inference(subst, [],
% 1.37/1.58 [refute_0_4 :
% 1.37/1.58 [bind(X, $fot(add(X_115, '==>'(0, X_116)))),
% 1.37/1.58 bind(Y, $fot(add('==>'(0, X_116), X_115)))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_85, plain,
% 1.37/1.58 (add('==>'(0, X_116), X_115) = add(X_115, '==>'(0, X_116))),
% 1.37/1.58 inference(resolve,
% 1.37/1.58 [$cnf($equal(add(X_115, '==>'(0, X_116)),
% 1.37/1.58 add('==>'(0, X_116), X_115)))],
% 1.37/1.58 [refute_0_83, refute_0_84])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_86, plain,
% 1.37/1.58 (add('==>'(0, X_116), X_115) != add(X_115, '==>'(0, X_116)) |
% 1.37/1.58 ~ greater_equal(add('==>'(0, X_116), X_115), add(X_116, X_115)) |
% 1.37/1.58 greater_equal(add(X_115, '==>'(0, X_116)), add(X_116, X_115))),
% 1.37/1.58 introduced(tautology,
% 1.37/1.58 [equality,
% 1.37/1.58 [$cnf(greater_equal(add('==>'(0, X_116), X_115),
% 1.37/1.58 add(X_116, X_115))), [0],
% 1.37/1.58 $fot(add(X_115, '==>'(0, X_116)))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_87, plain,
% 1.37/1.58 (~ greater_equal(add('==>'(0, X_116), X_115), add(X_116, X_115)) |
% 1.37/1.58 greater_equal(add(X_115, '==>'(0, X_116)), add(X_116, X_115))),
% 1.37/1.58 inference(resolve,
% 1.37/1.58 [$cnf($equal(add('==>'(0, X_116), X_115),
% 1.37/1.58 add(X_115, '==>'(0, X_116))))],
% 1.37/1.58 [refute_0_85, refute_0_86])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_88, plain,
% 1.37/1.58 (greater_equal(add(X_115, '==>'(0, X_116)), add(X_116, X_115))),
% 1.37/1.58 inference(resolve,
% 1.37/1.58 [$cnf(greater_equal(add('==>'(0, X_116), X_115),
% 1.37/1.58 add(X_116, X_115)))], [refute_0_82, refute_0_87])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_89, plain,
% 1.37/1.58 (~ greater_equal(add(X_115, '==>'(0, X_116)), add(X_116, X_115)) |
% 1.37/1.58 ~ greater_equal(add(X_116, X_115), add(X_115, '==>'(0, X_116))) |
% 1.37/1.58 add(X_115, '==>'(0, X_116)) = add(X_116, X_115)),
% 1.37/1.58 inference(subst, [],
% 1.37/1.58 [refute_0_28 :
% 1.37/1.58 [bind(X3, $fot(add(X_115, '==>'(0, X_116)))),
% 1.37/1.58 bind(X4, $fot(add(X_116, X_115)))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_90, plain,
% 1.37/1.58 (~ greater_equal(add(X_116, X_115), add(X_115, '==>'(0, X_116))) |
% 1.37/1.58 add(X_115, '==>'(0, X_116)) = add(X_116, X_115)),
% 1.37/1.58 inference(resolve,
% 1.37/1.58 [$cnf(greater_equal(add(X_115, '==>'(0, X_116)),
% 1.37/1.58 add(X_116, X_115)))], [refute_0_88, refute_0_89])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_91, plain,
% 1.37/1.58 (~ greater_equal(X_131, '==>'(X_130, X_131)) |
% 1.37/1.58 greater_equal(add(X_131, X10), add('==>'(X_130, X_131), X10))),
% 1.37/1.58 inference(subst, [],
% 1.37/1.58 [refute_0_33 :
% 1.37/1.58 [bind(X8, $fot(X_131)),
% 1.37/1.58 bind(X9, $fot('==>'(X_130, X_131)))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_92, plain, (greater_equal(X_131, '==>'(X_130, X_131))),
% 1.37/1.58 inference(subst, [],
% 1.37/1.58 [refute_0_43 :
% 1.37/1.58 [bind(X_123, $fot(X_130)), bind(X_125, $fot(X_131))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_93, plain,
% 1.37/1.58 (greater_equal(add(X_131, X10), add('==>'(X_130, X_131), X10))),
% 1.37/1.58 inference(resolve, [$cnf(greater_equal(X_131, '==>'(X_130, X_131)))],
% 1.37/1.58 [refute_0_92, refute_0_91])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_94, plain,
% 1.37/1.58 (greater_equal(add(X_181, X_179), add('==>'(X_180, X_181), X_179))),
% 1.37/1.58 inference(subst, [],
% 1.37/1.58 [refute_0_93 :
% 1.37/1.58 [bind(X10, $fot(X_179)), bind(X_130, $fot(X_180)),
% 1.37/1.58 bind(X_131, $fot(X_181))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_95, plain,
% 1.37/1.58 (add(X_179, '==>'(X_180, X_181)) = add('==>'(X_180, X_181), X_179)),
% 1.37/1.58 inference(subst, [],
% 1.37/1.58 [refute_0_18 :
% 1.37/1.58 [bind(A, $fot(X_179)),
% 1.37/1.58 bind(B, $fot('==>'(X_180, X_181)))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_96, plain,
% 1.37/1.58 (add(X_179, '==>'(X_180, X_181)) != add('==>'(X_180, X_181), X_179) |
% 1.37/1.58 add('==>'(X_180, X_181), X_179) = add(X_179, '==>'(X_180, X_181))),
% 1.37/1.58 inference(subst, [],
% 1.37/1.58 [refute_0_4 :
% 1.37/1.58 [bind(X, $fot(add(X_179, '==>'(X_180, X_181)))),
% 1.37/1.58 bind(Y, $fot(add('==>'(X_180, X_181), X_179)))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_97, plain,
% 1.37/1.58 (add('==>'(X_180, X_181), X_179) = add(X_179, '==>'(X_180, X_181))),
% 1.37/1.58 inference(resolve,
% 1.37/1.58 [$cnf($equal(add(X_179, '==>'(X_180, X_181)),
% 1.37/1.58 add('==>'(X_180, X_181), X_179)))],
% 1.37/1.58 [refute_0_95, refute_0_96])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_98, plain,
% 1.37/1.58 (add('==>'(X_180, X_181), X_179) != add(X_179, '==>'(X_180, X_181)) |
% 1.37/1.58 ~ greater_equal(add(X_181, X_179), add('==>'(X_180, X_181), X_179)) |
% 1.37/1.58 greater_equal(add(X_181, X_179), add(X_179, '==>'(X_180, X_181)))),
% 1.37/1.58 introduced(tautology,
% 1.37/1.58 [equality,
% 1.37/1.58 [$cnf(greater_equal(add(X_181, X_179),
% 1.37/1.58 add('==>'(X_180, X_181), X_179))), [1],
% 1.37/1.58 $fot(add(X_179, '==>'(X_180, X_181)))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_99, plain,
% 1.37/1.58 (~ greater_equal(add(X_181, X_179), add('==>'(X_180, X_181), X_179)) |
% 1.37/1.58 greater_equal(add(X_181, X_179), add(X_179, '==>'(X_180, X_181)))),
% 1.37/1.58 inference(resolve,
% 1.37/1.58 [$cnf($equal(add('==>'(X_180, X_181), X_179),
% 1.37/1.58 add(X_179, '==>'(X_180, X_181))))],
% 1.37/1.58 [refute_0_97, refute_0_98])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_100, plain,
% 1.37/1.58 (greater_equal(add(X_181, X_179), add(X_179, '==>'(X_180, X_181)))),
% 1.37/1.58 inference(resolve,
% 1.37/1.58 [$cnf(greater_equal(add(X_181, X_179),
% 1.37/1.58 add('==>'(X_180, X_181), X_179)))],
% 1.37/1.58 [refute_0_94, refute_0_99])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_101, plain,
% 1.37/1.58 (greater_equal(add(X_116, X_115), add(X_115, '==>'(0, X_116)))),
% 1.37/1.58 inference(subst, [],
% 1.37/1.58 [refute_0_100 :
% 1.37/1.58 [bind(X_179, $fot(X_115)), bind(X_180, $fot(0)),
% 1.37/1.58 bind(X_181, $fot(X_116))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_102, plain, (add(X_115, '==>'(0, X_116)) = add(X_116, X_115)),
% 1.37/1.58 inference(resolve,
% 1.37/1.58 [$cnf(greater_equal(add(X_116, X_115),
% 1.37/1.58 add(X_115, '==>'(0, X_116))))],
% 1.37/1.58 [refute_0_101, refute_0_90])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_103, plain, ('==>'(0, X_116) = X_116),
% 1.37/1.58 inference(subst, [], [refute_0_45 : [bind(X_344, $fot(X_116))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_104, plain,
% 1.37/1.58 (add(X_115, '==>'(0, X_116)) = add(X_115, '==>'(0, X_116))),
% 1.37/1.58 introduced(tautology, [refl, [$fot(add(X_115, '==>'(0, X_116)))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_105, plain,
% 1.37/1.58 (add(X_115, '==>'(0, X_116)) != add(X_115, '==>'(0, X_116)) |
% 1.37/1.58 '==>'(0, X_116) != X_116 |
% 1.37/1.58 add(X_115, '==>'(0, X_116)) = add(X_115, X_116)),
% 1.37/1.58 introduced(tautology,
% 1.37/1.58 [equality,
% 1.37/1.58 [$cnf($equal(add(X_115, '==>'(0, X_116)),
% 1.37/1.58 add(X_115, '==>'(0, X_116)))), [1, 1],
% 1.37/1.58 $fot(X_116)]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_106, plain,
% 1.37/1.58 ('==>'(0, X_116) != X_116 |
% 1.37/1.58 add(X_115, '==>'(0, X_116)) = add(X_115, X_116)),
% 1.37/1.58 inference(resolve,
% 1.37/1.58 [$cnf($equal(add(X_115, '==>'(0, X_116)),
% 1.37/1.58 add(X_115, '==>'(0, X_116))))],
% 1.37/1.58 [refute_0_104, refute_0_105])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_107, plain, (add(X_115, '==>'(0, X_116)) = add(X_115, X_116)),
% 1.37/1.58 inference(resolve, [$cnf($equal('==>'(0, X_116), X_116))],
% 1.37/1.58 [refute_0_103, refute_0_106])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_108, plain,
% 1.37/1.58 (add(X_115, '==>'(0, X_116)) != add(X_115, X_116) |
% 1.37/1.58 add(X_115, '==>'(0, X_116)) != add(X_116, X_115) |
% 1.37/1.58 add(X_115, X_116) = add(X_116, X_115)),
% 1.37/1.58 introduced(tautology,
% 1.37/1.58 [equality,
% 1.37/1.58 [$cnf($equal(add(X_115, '==>'(0, X_116)),
% 1.37/1.58 add(X_116, X_115))), [0],
% 1.37/1.58 $fot(add(X_115, X_116))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_109, plain,
% 1.37/1.58 (add(X_115, '==>'(0, X_116)) != add(X_116, X_115) |
% 1.37/1.58 add(X_115, X_116) = add(X_116, X_115)),
% 1.37/1.58 inference(resolve,
% 1.37/1.58 [$cnf($equal(add(X_115, '==>'(0, X_116)),
% 1.37/1.58 add(X_115, X_116)))], [refute_0_107, refute_0_108])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_110, plain, (add(X_115, X_116) = add(X_116, X_115)),
% 1.37/1.58 inference(resolve,
% 1.37/1.58 [$cnf($equal(add(X_115, '==>'(0, X_116)),
% 1.37/1.58 add(X_116, X_115)))], [refute_0_102, refute_0_109])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_111, plain,
% 1.37/1.58 (add(X_115, X_116) != add(X_116, X_115) |
% 1.37/1.58 add(X_116, X_115) = add(X_115, X_116)),
% 1.37/1.58 inference(subst, [],
% 1.37/1.58 [refute_0_4 :
% 1.37/1.58 [bind(X, $fot(add(X_115, X_116))),
% 1.37/1.58 bind(Y, $fot(add(X_116, X_115)))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_112, plain, (add(X_116, X_115) = add(X_115, X_116)),
% 1.37/1.58 inference(resolve,
% 1.37/1.58 [$cnf($equal(add(X_115, X_116), add(X_116, X_115)))],
% 1.37/1.58 [refute_0_110, refute_0_111])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_113, plain,
% 1.37/1.58 (add('==>'(1, X_227), 0) = add(0, '==>'(1, X_227))),
% 1.37/1.58 inference(subst, [],
% 1.37/1.58 [refute_0_112 :
% 1.37/1.58 [bind(X_115, $fot(0)),
% 1.37/1.58 bind(X_116, $fot('==>'(1, X_227)))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_114, plain, (Y != X | Y != Z | X = Z),
% 1.37/1.58 introduced(tautology, [equality, [$cnf($equal(Y, Z)), [0], $fot(X)]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_115, plain, (X != Y | Y != Z | X = Z),
% 1.37/1.58 inference(resolve, [$cnf($equal(Y, X))], [refute_0_4, refute_0_114])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_116, plain,
% 1.37/1.58 (add(0, '==>'(1, X_227)) != '==>'(1, X_227) |
% 1.37/1.58 add('==>'(1, X_227), 0) != add(0, '==>'(1, X_227)) |
% 1.37/1.58 add('==>'(1, X_227), 0) = '==>'(1, X_227)),
% 1.37/1.58 inference(subst, [],
% 1.37/1.58 [refute_0_115 :
% 1.37/1.58 [bind(X, $fot(add('==>'(1, X_227), 0))),
% 1.37/1.58 bind(Y, $fot(add(0, '==>'(1, X_227)))),
% 1.37/1.58 bind(Z, $fot('==>'(1, X_227)))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_117, plain,
% 1.37/1.58 (add(0, '==>'(1, X_227)) != '==>'(1, X_227) |
% 1.37/1.58 add('==>'(1, X_227), 0) = '==>'(1, X_227)),
% 1.37/1.58 inference(resolve,
% 1.37/1.58 [$cnf($equal(add('==>'(1, X_227), 0),
% 1.37/1.58 add(0, '==>'(1, X_227))))],
% 1.37/1.58 [refute_0_113, refute_0_116])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_118, plain, (add('==>'(1, X_227), 0) = '==>'(1, X_227)),
% 1.37/1.58 inference(resolve,
% 1.37/1.58 [$cnf($equal(add(0, '==>'(1, X_227)), '==>'(1, X_227)))],
% 1.37/1.58 [refute_0_78, refute_0_117])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_119, plain,
% 1.37/1.58 (add('==>'(1, X_227), 0) != 0 |
% 1.37/1.58 add('==>'(1, X_227), 0) != '==>'(1, X_227) | '==>'(1, X_227) = 0),
% 1.37/1.58 introduced(tautology,
% 1.37/1.58 [equality,
% 1.37/1.58 [$cnf($equal(add('==>'(1, X_227), 0), 0)), [0],
% 1.37/1.58 $fot('==>'(1, X_227))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_120, plain,
% 1.37/1.58 (add('==>'(1, X_227), 0) != 0 | '==>'(1, X_227) = 0),
% 1.37/1.58 inference(resolve,
% 1.37/1.58 [$cnf($equal(add('==>'(1, X_227), 0), '==>'(1, X_227)))],
% 1.37/1.58 [refute_0_118, refute_0_119])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_121, plain, ('==>'(1, X_227) = 0),
% 1.37/1.58 inference(resolve, [$cnf($equal(add('==>'(1, X_227), 0), 0))],
% 1.37/1.58 [refute_0_77, refute_0_120])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_122, plain, ('==>'(1, skolemFOFtoCNF_X17) = 0),
% 1.37/1.58 inference(subst, [],
% 1.37/1.58 [refute_0_121 : [bind(X_227, $fot(skolemFOFtoCNF_X17))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_123, plain,
% 1.37/1.58 ('==>'('==>'(1, skolemFOFtoCNF_X17), skolemFOFtoCNF_X17) =
% 1.37/1.58 '==>'('==>'(1, skolemFOFtoCNF_X17), skolemFOFtoCNF_X17)),
% 1.37/1.58 introduced(tautology,
% 1.37/1.58 [refl,
% 1.37/1.58 [$fot('==>'('==>'(1, skolemFOFtoCNF_X17),
% 1.37/1.58 skolemFOFtoCNF_X17))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_124, plain,
% 1.37/1.58 ('==>'(1, skolemFOFtoCNF_X17) != 0 |
% 1.37/1.58 '==>'('==>'(1, skolemFOFtoCNF_X17), skolemFOFtoCNF_X17) !=
% 1.37/1.58 '==>'('==>'(1, skolemFOFtoCNF_X17), skolemFOFtoCNF_X17) |
% 1.37/1.58 '==>'('==>'(1, skolemFOFtoCNF_X17), skolemFOFtoCNF_X17) =
% 1.37/1.58 '==>'(0, skolemFOFtoCNF_X17)),
% 1.37/1.58 introduced(tautology,
% 1.37/1.58 [equality,
% 1.37/1.58 [$cnf($equal('==>'('==>'(1, skolemFOFtoCNF_X17),
% 1.37/1.58 skolemFOFtoCNF_X17),
% 1.37/1.58 '==>'('==>'(1, skolemFOFtoCNF_X17),
% 1.37/1.58 skolemFOFtoCNF_X17))), [1, 0], $fot(0)]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_125, plain,
% 1.37/1.58 ('==>'(1, skolemFOFtoCNF_X17) != 0 |
% 1.37/1.58 '==>'('==>'(1, skolemFOFtoCNF_X17), skolemFOFtoCNF_X17) =
% 1.37/1.58 '==>'(0, skolemFOFtoCNF_X17)),
% 1.37/1.58 inference(resolve,
% 1.37/1.58 [$cnf($equal('==>'('==>'(1, skolemFOFtoCNF_X17),
% 1.37/1.58 skolemFOFtoCNF_X17),
% 1.37/1.58 '==>'('==>'(1, skolemFOFtoCNF_X17),
% 1.37/1.58 skolemFOFtoCNF_X17)))],
% 1.37/1.58 [refute_0_123, refute_0_124])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_126, plain,
% 1.37/1.58 ('==>'('==>'(1, skolemFOFtoCNF_X17), skolemFOFtoCNF_X17) =
% 1.37/1.58 '==>'(0, skolemFOFtoCNF_X17)),
% 1.37/1.58 inference(resolve, [$cnf($equal('==>'(1, skolemFOFtoCNF_X17), 0))],
% 1.37/1.58 [refute_0_122, refute_0_125])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_127, plain,
% 1.37/1.58 ('==>'(0, skolemFOFtoCNF_X17) != skolemFOFtoCNF_X17 |
% 1.37/1.58 '==>'('==>'(1, skolemFOFtoCNF_X17), skolemFOFtoCNF_X17) !=
% 1.37/1.58 '==>'(0, skolemFOFtoCNF_X17) |
% 1.37/1.58 '==>'('==>'(1, skolemFOFtoCNF_X17), skolemFOFtoCNF_X17) =
% 1.37/1.58 skolemFOFtoCNF_X17),
% 1.37/1.58 inference(subst, [],
% 1.37/1.58 [refute_0_115 :
% 1.37/1.58 [bind(X,
% 1.37/1.58 $fot('==>'('==>'(1, skolemFOFtoCNF_X17),
% 1.37/1.58 skolemFOFtoCNF_X17))),
% 1.37/1.58 bind(Y, $fot('==>'(0, skolemFOFtoCNF_X17))),
% 1.37/1.58 bind(Z, $fot(skolemFOFtoCNF_X17))]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_128, plain,
% 1.37/1.58 ('==>'(0, skolemFOFtoCNF_X17) != skolemFOFtoCNF_X17 |
% 1.37/1.58 '==>'('==>'(1, skolemFOFtoCNF_X17), skolemFOFtoCNF_X17) =
% 1.37/1.58 skolemFOFtoCNF_X17),
% 1.37/1.58 inference(resolve,
% 1.37/1.58 [$cnf($equal('==>'('==>'(1, skolemFOFtoCNF_X17),
% 1.37/1.58 skolemFOFtoCNF_X17),
% 1.37/1.58 '==>'(0, skolemFOFtoCNF_X17)))],
% 1.37/1.58 [refute_0_126, refute_0_127])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_129, plain,
% 1.37/1.58 ('==>'('==>'(1, skolemFOFtoCNF_X17), skolemFOFtoCNF_X17) =
% 1.37/1.58 skolemFOFtoCNF_X17),
% 1.37/1.58 inference(resolve,
% 1.37/1.58 [$cnf($equal('==>'(0, skolemFOFtoCNF_X17),
% 1.37/1.58 skolemFOFtoCNF_X17))], [refute_0_46, refute_0_128])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_130, plain,
% 1.37/1.58 ('==>'('==>'(1, skolemFOFtoCNF_X17), skolemFOFtoCNF_X17) !=
% 1.37/1.58 skolemFOFtoCNF_X17 | skolemFOFtoCNF_X17 != skolemFOFtoCNF_X17 |
% 1.37/1.58 '==>'('==>'(1, skolemFOFtoCNF_X17), skolemFOFtoCNF_X17) =
% 1.37/1.58 skolemFOFtoCNF_X17),
% 1.37/1.58 introduced(tautology,
% 1.37/1.58 [equality,
% 1.37/1.58 [$cnf(~ $equal('==>'('==>'(1, skolemFOFtoCNF_X17),
% 1.37/1.58 skolemFOFtoCNF_X17), skolemFOFtoCNF_X17)), [0],
% 1.37/1.58 $fot(skolemFOFtoCNF_X17)]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_131, plain,
% 1.37/1.58 (skolemFOFtoCNF_X17 != skolemFOFtoCNF_X17 |
% 1.37/1.58 '==>'('==>'(1, skolemFOFtoCNF_X17), skolemFOFtoCNF_X17) =
% 1.37/1.58 skolemFOFtoCNF_X17),
% 1.37/1.58 inference(resolve,
% 1.37/1.58 [$cnf($equal('==>'('==>'(1, skolemFOFtoCNF_X17),
% 1.37/1.58 skolemFOFtoCNF_X17), skolemFOFtoCNF_X17))],
% 1.37/1.58 [refute_0_129, refute_0_130])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_132, plain, (skolemFOFtoCNF_X17 != skolemFOFtoCNF_X17),
% 1.37/1.58 inference(resolve,
% 1.37/1.58 [$cnf($equal('==>'('==>'(1, skolemFOFtoCNF_X17),
% 1.37/1.58 skolemFOFtoCNF_X17), skolemFOFtoCNF_X17))],
% 1.37/1.58 [refute_0_131, refute_0_10])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_133, plain, (skolemFOFtoCNF_X17 = skolemFOFtoCNF_X17),
% 1.37/1.58 introduced(tautology, [refl, [$fot(skolemFOFtoCNF_X17)]])).
% 1.37/1.58
% 1.37/1.58 cnf(refute_0_134, plain, ($false),
% 1.37/1.58 inference(resolve,
% 1.37/1.58 [$cnf($equal(skolemFOFtoCNF_X17, skolemFOFtoCNF_X17))],
% 1.37/1.58 [refute_0_133, refute_0_132])).
% 1.37/1.58 % SZS output end CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.37/1.58
%------------------------------------------------------------------------------