TSTP Solution File: LCL902+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL902+1 : TPTP v8.1.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% 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 : 600s
% DateTime : Sun Jul 17 12:56:52 EDT 2022
% Result : Theorem 3.51s 3.70s
% Output : CNFRefutation 3.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LCL902+1 : TPTP v8.1.0. Released v5.5.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.11/0.33 % Computer : n006.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 : Sat Jul 2 15:10:07 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 3.51/3.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.51/3.70
% 3.51/3.70 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.51/3.70 fof(sos_01, axiom, (! [A, B, C] : add(add(A, B), C) = add(A, add(B, C)))).
% 3.51/3.70
% 3.51/3.70 fof(sos_02, axiom, (! [A, B] : add(A, B) = add(B, A))).
% 3.51/3.70
% 3.51/3.70 fof(sos_03, axiom, (! [A] : add(A, 0) = A)).
% 3.51/3.70
% 3.51/3.70 fof(sos_04, axiom, (! [A] : greater_equal(A, A))).
% 3.51/3.70
% 3.51/3.70 fof(sos_06, axiom,
% 3.51/3.70 (! [X3, X4] :
% 3.51/3.70 ((greater_equal(X3, X4) & greater_equal(X4, X3)) => X3 = X4))).
% 3.51/3.70
% 3.51/3.70 fof(sos_07, axiom,
% 3.51/3.70 (! [X5, X6, X7] :
% 3.51/3.70 (greater_equal(add(X5, X6), X7) <=>
% 3.51/3.70 greater_equal(X6, '==>'(X5, X7))))).
% 3.51/3.70
% 3.51/3.70 fof(sos_08, axiom, (! [A] : greater_equal(A, 0))).
% 3.51/3.70
% 3.51/3.70 fof(sos_09, axiom,
% 3.51/3.70 (! [X8, X9, X10] :
% 3.51/3.70 (greater_equal(X8, X9) =>
% 3.51/3.70 greater_equal(add(X8, X10), add(X9, X10))))).
% 3.51/3.70
% 3.51/3.70 fof(sos_11, axiom,
% 3.51/3.70 (! [X14, X15, X16] :
% 3.51/3.70 (greater_equal(X14, X15) =>
% 3.51/3.70 greater_equal('==>'(X16, X14), '==>'(X16, X15))))).
% 3.51/3.70
% 3.51/3.70 fof(sos_12, axiom, (! [A] : add(A, 1) = 1)).
% 3.51/3.70
% 3.51/3.70 fof(sos_13, axiom, (! [A] : '==>'('==>'('==>'(A, 1), A), A) = 0)).
% 3.51/3.70
% 3.51/3.70 fof(goals_14, conjecture, (! [X17] : '==>'('==>'(X17, 1), 1) = X17)).
% 3.51/3.70
% 3.51/3.70 fof(subgoal_0, plain, (! [X17] : '==>'('==>'(X17, 1), 1) = X17),
% 3.51/3.70 inference(strip, [], [goals_14])).
% 3.51/3.70
% 3.51/3.70 fof(negate_0_0, plain, (~ ! [X17] : '==>'('==>'(X17, 1), 1) = X17),
% 3.51/3.70 inference(negate, [], [subgoal_0])).
% 3.51/3.70
% 3.51/3.70 fof(normalize_0_0, plain, (? [X17] : '==>'('==>'(X17, 1), 1) != X17),
% 3.51/3.70 inference(canonicalize, [], [negate_0_0])).
% 3.51/3.70
% 3.51/3.70 fof(normalize_0_1, plain,
% 3.51/3.70 ('==>'('==>'(skolemFOFtoCNF_X17, 1), 1) != skolemFOFtoCNF_X17),
% 3.51/3.70 inference(skolemize, [], [normalize_0_0])).
% 3.51/3.70
% 3.51/3.70 fof(normalize_0_2, plain, (! [A] : add(A, 0) = A),
% 3.51/3.70 inference(canonicalize, [], [sos_03])).
% 3.51/3.70
% 3.51/3.70 fof(normalize_0_3, plain, (! [A] : add(A, 0) = A),
% 3.51/3.70 inference(specialize, [], [normalize_0_2])).
% 3.51/3.70
% 3.51/3.70 fof(normalize_0_4, plain,
% 3.51/3.70 (! [X3, X4] :
% 3.51/3.70 (~ greater_equal(X3, X4) | ~ greater_equal(X4, X3) | X3 = X4)),
% 3.51/3.70 inference(canonicalize, [], [sos_06])).
% 3.51/3.70
% 3.51/3.70 fof(normalize_0_5, plain,
% 3.51/3.70 (! [X3, X4] :
% 3.51/3.70 (~ greater_equal(X3, X4) | ~ greater_equal(X4, X3) | X3 = X4)),
% 3.51/3.70 inference(specialize, [], [normalize_0_4])).
% 3.51/3.70
% 3.51/3.70 fof(normalize_0_6, plain,
% 3.51/3.70 (! [X8, X9] :
% 3.51/3.70 (~ greater_equal(X8, X9) |
% 3.51/3.70 ! [X10] : greater_equal(add(X8, X10), add(X9, X10)))),
% 3.51/3.70 inference(canonicalize, [], [sos_09])).
% 3.51/3.70
% 3.51/3.70 fof(normalize_0_7, plain,
% 3.51/3.70 (! [X8, X9] :
% 3.51/3.70 (~ greater_equal(X8, X9) |
% 3.51/3.70 ! [X10] : greater_equal(add(X8, X10), add(X9, X10)))),
% 3.51/3.70 inference(specialize, [], [normalize_0_6])).
% 3.51/3.70
% 3.51/3.70 fof(normalize_0_8, plain,
% 3.51/3.70 (! [X10, X8, X9] :
% 3.51/3.70 (~ greater_equal(X8, X9) |
% 3.51/3.70 greater_equal(add(X8, X10), add(X9, X10)))),
% 3.51/3.70 inference(clausify, [], [normalize_0_7])).
% 3.51/3.70
% 3.51/3.70 fof(normalize_0_9, plain, (! [A] : greater_equal(A, 0)),
% 3.51/3.70 inference(canonicalize, [], [sos_08])).
% 3.51/3.70
% 3.51/3.70 fof(normalize_0_10, plain, (! [A] : greater_equal(A, 0)),
% 3.51/3.70 inference(specialize, [], [normalize_0_9])).
% 3.51/3.70
% 3.51/3.70 fof(normalize_0_11, plain, (! [A, B] : add(A, B) = add(B, A)),
% 3.51/3.70 inference(canonicalize, [], [sos_02])).
% 3.51/3.70
% 3.51/3.70 fof(normalize_0_12, plain, (! [A, B] : add(A, B) = add(B, A)),
% 3.51/3.70 inference(specialize, [], [normalize_0_11])).
% 3.51/3.70
% 3.51/3.70 fof(normalize_0_13, plain, (! [A] : add(A, 1) = 1),
% 3.51/3.70 inference(canonicalize, [], [sos_12])).
% 3.51/3.70
% 3.51/3.70 fof(normalize_0_14, plain, (! [A] : add(A, 1) = 1),
% 3.51/3.70 inference(specialize, [], [normalize_0_13])).
% 3.51/3.70
% 3.51/3.70 fof(normalize_0_15, plain,
% 3.51/3.70 (! [X14, X15] :
% 3.51/3.70 (~ greater_equal(X14, X15) |
% 3.51/3.70 ! [X16] : greater_equal('==>'(X16, X14), '==>'(X16, X15)))),
% 3.51/3.70 inference(canonicalize, [], [sos_11])).
% 3.51/3.70
% 3.51/3.70 fof(normalize_0_16, plain,
% 3.51/3.70 (! [X14, X15] :
% 3.51/3.70 (~ greater_equal(X14, X15) |
% 3.51/3.70 ! [X16] : greater_equal('==>'(X16, X14), '==>'(X16, X15)))),
% 3.51/3.70 inference(specialize, [], [normalize_0_15])).
% 3.51/3.70
% 3.51/3.70 fof(normalize_0_17, plain,
% 3.51/3.70 (! [X14, X15, X16] :
% 3.51/3.70 (~ greater_equal(X14, X15) |
% 3.51/3.70 greater_equal('==>'(X16, X14), '==>'(X16, X15)))),
% 3.51/3.70 inference(clausify, [], [normalize_0_16])).
% 3.51/3.70
% 3.51/3.70 fof(normalize_0_18, plain,
% 3.51/3.70 (! [X5, X6, X7] :
% 3.51/3.70 (~ greater_equal(X6, '==>'(X5, X7)) <=>
% 3.51/3.70 ~ greater_equal(add(X5, X6), X7))),
% 3.51/3.70 inference(canonicalize, [], [sos_07])).
% 3.51/3.70
% 3.51/3.70 fof(normalize_0_19, plain,
% 3.51/3.70 (! [X5, X6, X7] :
% 3.51/3.70 (~ greater_equal(X6, '==>'(X5, X7)) <=>
% 3.51/3.70 ~ greater_equal(add(X5, X6), X7))),
% 3.51/3.70 inference(specialize, [], [normalize_0_18])).
% 3.51/3.71
% 3.51/3.71 fof(normalize_0_20, plain,
% 3.51/3.71 (! [X5, X6, X7] :
% 3.51/3.71 ((~ greater_equal(X6, '==>'(X5, X7)) |
% 3.51/3.71 greater_equal(add(X5, X6), X7)) &
% 3.51/3.71 (~ greater_equal(add(X5, X6), X7) |
% 3.51/3.71 greater_equal(X6, '==>'(X5, X7))))),
% 3.51/3.71 inference(clausify, [], [normalize_0_19])).
% 3.51/3.71
% 3.51/3.71 fof(normalize_0_21, plain,
% 3.51/3.71 (! [X5, X6, X7] :
% 3.51/3.71 (~ greater_equal(X6, '==>'(X5, X7)) |
% 3.51/3.71 greater_equal(add(X5, X6), X7))),
% 3.51/3.71 inference(conjunct, [], [normalize_0_20])).
% 3.51/3.71
% 3.51/3.71 fof(normalize_0_22, plain, (! [A] : greater_equal(A, A)),
% 3.51/3.71 inference(canonicalize, [], [sos_04])).
% 3.51/3.71
% 3.51/3.71 fof(normalize_0_23, plain, (! [A] : greater_equal(A, A)),
% 3.51/3.71 inference(specialize, [], [normalize_0_22])).
% 3.51/3.71
% 3.51/3.71 fof(normalize_0_24, plain, (! [A] : '==>'('==>'('==>'(A, 1), A), A) = 0),
% 3.51/3.71 inference(canonicalize, [], [sos_13])).
% 3.51/3.71
% 3.51/3.71 fof(normalize_0_25, plain, (! [A] : '==>'('==>'('==>'(A, 1), A), A) = 0),
% 3.51/3.71 inference(specialize, [], [normalize_0_24])).
% 3.51/3.71
% 3.51/3.71 fof(normalize_0_26, plain,
% 3.51/3.71 (! [X5, X6, X7] :
% 3.51/3.71 (~ greater_equal(add(X5, X6), X7) |
% 3.51/3.71 greater_equal(X6, '==>'(X5, X7)))),
% 3.51/3.71 inference(conjunct, [], [normalize_0_20])).
% 3.51/3.71
% 3.51/3.71 fof(normalize_0_27, plain,
% 3.51/3.71 (! [A, B, C] : add(add(A, B), C) = add(A, add(B, C))),
% 3.51/3.71 inference(canonicalize, [], [sos_01])).
% 3.51/3.71
% 3.51/3.71 fof(normalize_0_28, plain,
% 3.51/3.71 (! [A, B, C] : add(add(A, B), C) = add(A, add(B, C))),
% 3.51/3.71 inference(specialize, [], [normalize_0_27])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_0, plain,
% 3.51/3.71 ('==>'('==>'(skolemFOFtoCNF_X17, 1), 1) != skolemFOFtoCNF_X17),
% 3.51/3.71 inference(canonicalize, [], [normalize_0_1])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_1, plain, (add(A, 0) = A),
% 3.51/3.71 inference(canonicalize, [], [normalize_0_3])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_2, plain,
% 3.51/3.71 (add('==>'('==>'(X_628, 1), 1), 0) = '==>'('==>'(X_628, 1), 1)),
% 3.51/3.71 inference(subst, [],
% 3.51/3.71 [refute_0_1 : [bind(A, $fot('==>'('==>'(X_628, 1), 1)))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_3, plain,
% 3.51/3.71 (~ greater_equal(X3, X4) | ~ greater_equal(X4, X3) | X3 = X4),
% 3.51/3.71 inference(canonicalize, [], [normalize_0_5])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_4, plain,
% 3.51/3.71 (~
% 3.51/3.71 greater_equal(add(X_512, X_511),
% 3.51/3.71 add('==>'('==>'(X_512, 1), 1), X_511)) |
% 3.51/3.71 ~
% 3.51/3.71 greater_equal(add('==>'('==>'(X_512, 1), 1), X_511),
% 3.51/3.71 add(X_512, X_511)) |
% 3.51/3.71 add(X_512, X_511) = add('==>'('==>'(X_512, 1), 1), X_511)),
% 3.51/3.71 inference(subst, [],
% 3.51/3.71 [refute_0_3 :
% 3.51/3.71 [bind(X3, $fot(add(X_512, X_511))),
% 3.51/3.71 bind(X4, $fot(add('==>'('==>'(X_512, 1), 1), X_511)))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_5, plain,
% 3.51/3.71 (~ greater_equal(X8, X9) | greater_equal(add(X8, X10), add(X9, X10))),
% 3.51/3.71 inference(canonicalize, [], [normalize_0_8])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_6, plain,
% 3.51/3.71 (~ greater_equal('==>'('==>'(X_451, 1), 1), X_451) |
% 3.51/3.71 greater_equal(add('==>'('==>'(X_451, 1), 1), X10), add(X_451, X10))),
% 3.51/3.71 inference(subst, [],
% 3.51/3.71 [refute_0_5 :
% 3.51/3.71 [bind(X8, $fot('==>'('==>'(X_451, 1), 1))),
% 3.51/3.71 bind(X9, $fot(X_451))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_7, plain, (greater_equal(A, 0)),
% 3.51/3.71 inference(canonicalize, [], [normalize_0_10])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_8, plain, (greater_equal(X_22, 0)),
% 3.51/3.71 inference(subst, [], [refute_0_7 : [bind(A, $fot(X_22))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_9, plain,
% 3.51/3.71 (~ greater_equal(X_22, 0) |
% 3.51/3.71 greater_equal(add(X_22, X_21), add(0, X_21))),
% 3.51/3.71 inference(subst, [],
% 3.51/3.71 [refute_0_5 :
% 3.51/3.71 [bind(X10, $fot(X_21)), bind(X8, $fot(X_22)),
% 3.51/3.71 bind(X9, $fot(0))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_10, plain, (greater_equal(add(X_22, X_21), add(0, X_21))),
% 3.51/3.71 inference(resolve, [$cnf(greater_equal(X_22, 0))],
% 3.51/3.71 [refute_0_8, refute_0_9])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_11, plain, (add(A, B) = add(B, A)),
% 3.51/3.71 inference(canonicalize, [], [normalize_0_12])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_12, plain, (add(A, 0) = add(0, A)),
% 3.51/3.71 inference(subst, [], [refute_0_11 : [bind(B, $fot(0))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_13, plain,
% 3.51/3.71 (add(A, 0) != A | add(A, 0) != add(0, A) | add(0, A) = A),
% 3.51/3.71 introduced(tautology,
% 3.51/3.71 [equality,
% 3.51/3.71 [$cnf($equal(add(A, 0), A)), [0], $fot(add(0, A))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_14, plain, (add(A, 0) != A | add(0, A) = A),
% 3.51/3.71 inference(resolve, [$cnf($equal(add(A, 0), add(0, A)))],
% 3.51/3.71 [refute_0_12, refute_0_13])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_15, plain, (add(0, A) = A),
% 3.51/3.71 inference(resolve, [$cnf($equal(add(A, 0), A))],
% 3.51/3.71 [refute_0_1, refute_0_14])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_16, plain, (add(0, X_21) = X_21),
% 3.51/3.71 inference(subst, [], [refute_0_15 : [bind(A, $fot(X_21))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_17, plain,
% 3.51/3.71 (add(0, X_21) != X_21 |
% 3.51/3.71 ~ greater_equal(add(X_22, X_21), add(0, X_21)) |
% 3.51/3.71 greater_equal(add(X_22, X_21), X_21)),
% 3.51/3.71 introduced(tautology,
% 3.51/3.71 [equality,
% 3.51/3.71 [$cnf(greater_equal(add(X_22, X_21), add(0, X_21))), [1],
% 3.51/3.71 $fot(X_21)]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_18, plain,
% 3.51/3.71 (~ greater_equal(add(X_22, X_21), add(0, X_21)) |
% 3.51/3.71 greater_equal(add(X_22, X_21), X_21)),
% 3.51/3.71 inference(resolve, [$cnf($equal(add(0, X_21), X_21))],
% 3.51/3.71 [refute_0_16, refute_0_17])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_19, plain, (greater_equal(add(X_22, X_21), X_21)),
% 3.51/3.71 inference(resolve,
% 3.51/3.71 [$cnf(greater_equal(add(X_22, X_21), add(0, X_21)))],
% 3.51/3.71 [refute_0_10, refute_0_18])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_20, plain, (greater_equal(add(1, X_24), X_24)),
% 3.51/3.71 inference(subst, [],
% 3.51/3.71 [refute_0_19 :
% 3.51/3.71 [bind(X_21, $fot(X_24)), bind(X_22, $fot(1))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_21, plain, (add(A, 1) = 1),
% 3.51/3.71 inference(canonicalize, [], [normalize_0_14])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_22, plain, (add(A, 1) = add(1, A)),
% 3.51/3.71 inference(subst, [], [refute_0_11 : [bind(B, $fot(1))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_23, plain,
% 3.51/3.71 (add(A, 1) != add(1, A) | add(A, 1) != 1 | add(1, A) = 1),
% 3.51/3.71 introduced(tautology,
% 3.51/3.71 [equality,
% 3.51/3.71 [$cnf($equal(add(A, 1), 1)), [0], $fot(add(1, A))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_24, plain, (add(A, 1) != 1 | add(1, A) = 1),
% 3.51/3.71 inference(resolve, [$cnf($equal(add(A, 1), add(1, A)))],
% 3.51/3.71 [refute_0_22, refute_0_23])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_25, plain, (add(1, A) = 1),
% 3.51/3.71 inference(resolve, [$cnf($equal(add(A, 1), 1))],
% 3.51/3.71 [refute_0_21, refute_0_24])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_26, plain, (add(1, X_24) = 1),
% 3.51/3.71 inference(subst, [], [refute_0_25 : [bind(A, $fot(X_24))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_27, plain,
% 3.51/3.71 (add(1, X_24) != 1 | ~ greater_equal(add(1, X_24), X_24) |
% 3.51/3.71 greater_equal(1, X_24)),
% 3.51/3.71 introduced(tautology,
% 3.51/3.71 [equality,
% 3.51/3.71 [$cnf(greater_equal(add(1, X_24), X_24)), [0], $fot(1)]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_28, plain,
% 3.51/3.71 (~ greater_equal(add(1, X_24), X_24) | greater_equal(1, X_24)),
% 3.51/3.71 inference(resolve, [$cnf($equal(add(1, X_24), 1))],
% 3.51/3.71 [refute_0_26, refute_0_27])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_29, plain, (greater_equal(1, X_24)),
% 3.51/3.71 inference(resolve, [$cnf(greater_equal(add(1, X_24), X_24))],
% 3.51/3.71 [refute_0_20, refute_0_28])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_30, plain, (greater_equal(1, X_402)),
% 3.51/3.71 inference(subst, [], [refute_0_29 : [bind(X_24, $fot(X_402))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_31, plain,
% 3.51/3.71 (~ greater_equal(X14, X15) |
% 3.51/3.71 greater_equal('==>'(X16, X14), '==>'(X16, X15))),
% 3.51/3.71 inference(canonicalize, [], [normalize_0_17])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_32, plain,
% 3.51/3.71 (~ greater_equal(1, X_402) |
% 3.51/3.71 greater_equal('==>'(X_403, 1), '==>'(X_403, X_402))),
% 3.51/3.71 inference(subst, [],
% 3.51/3.71 [refute_0_31 :
% 3.51/3.71 [bind(X14, $fot(1)), bind(X15, $fot(X_402)),
% 3.51/3.71 bind(X16, $fot(X_403))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_33, plain,
% 3.51/3.71 (greater_equal('==>'(X_403, 1), '==>'(X_403, X_402))),
% 3.51/3.71 inference(resolve, [$cnf(greater_equal(1, X_402))],
% 3.51/3.71 [refute_0_30, refute_0_32])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_34, plain,
% 3.51/3.71 (greater_equal('==>'('==>'(X_402, 1), 1),
% 3.51/3.71 '==>'('==>'(X_402, 1), X_402))),
% 3.51/3.71 inference(subst, [],
% 3.51/3.71 [refute_0_33 : [bind(X_403, $fot('==>'(X_402, 1)))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_35, plain,
% 3.51/3.71 (~ greater_equal(X6, '==>'(X5, X7)) | greater_equal(add(X5, X6), X7)),
% 3.51/3.71 inference(canonicalize, [], [normalize_0_21])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_36, plain,
% 3.51/3.71 (~
% 3.51/3.71 greater_equal(add(X_87, '==>'(X_87, '==>'(X5, X7))),
% 3.51/3.71 '==>'(X5, X7)) |
% 3.51/3.71 greater_equal(add(X5, add(X_87, '==>'(X_87, '==>'(X5, X7)))), X7)),
% 3.51/3.71 inference(subst, [],
% 3.51/3.71 [refute_0_35 :
% 3.51/3.71 [bind(X6, $fot(add(X_87, '==>'(X_87, '==>'(X5, X7)))))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_37, plain, (greater_equal(A, A)),
% 3.51/3.71 inference(canonicalize, [], [normalize_0_23])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_38, plain,
% 3.51/3.71 (greater_equal('==>'(X_84, X_86), '==>'(X_84, X_86))),
% 3.51/3.71 inference(subst, [],
% 3.51/3.71 [refute_0_37 : [bind(A, $fot('==>'(X_84, X_86)))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_39, plain,
% 3.51/3.71 (~ greater_equal('==>'(X_84, X_86), '==>'(X_84, X_86)) |
% 3.51/3.71 greater_equal(add(X_84, '==>'(X_84, X_86)), X_86)),
% 3.51/3.71 inference(subst, [],
% 3.51/3.71 [refute_0_35 :
% 3.51/3.71 [bind(X5, $fot(X_84)), bind(X6, $fot('==>'(X_84, X_86))),
% 3.51/3.71 bind(X7, $fot(X_86))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_40, plain,
% 3.51/3.71 (greater_equal(add(X_84, '==>'(X_84, X_86)), X_86)),
% 3.51/3.71 inference(resolve,
% 3.51/3.71 [$cnf(greater_equal('==>'(X_84, X_86), '==>'(X_84, X_86)))],
% 3.51/3.71 [refute_0_38, refute_0_39])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_41, plain,
% 3.51/3.71 (greater_equal(add(X_87, '==>'(X_87, '==>'(X5, X7))), '==>'(X5, X7))),
% 3.51/3.71 inference(subst, [],
% 3.51/3.71 [refute_0_40 :
% 3.51/3.71 [bind(X_84, $fot(X_87)),
% 3.51/3.71 bind(X_86, $fot('==>'(X5, X7)))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_42, plain,
% 3.51/3.71 (greater_equal(add(X5, add(X_87, '==>'(X_87, '==>'(X5, X7)))), X7)),
% 3.51/3.71 inference(resolve,
% 3.51/3.71 [$cnf(greater_equal(add(X_87, '==>'(X_87, '==>'(X5, X7))),
% 3.51/3.71 '==>'(X5, X7)))], [refute_0_41, refute_0_36])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_43, plain,
% 3.51/3.71 (greater_equal(add(0, add(X_120, '==>'(X_120, '==>'(0, X_119)))),
% 3.51/3.71 X_119)),
% 3.51/3.71 inference(subst, [],
% 3.51/3.71 [refute_0_42 :
% 3.51/3.71 [bind(X5, $fot(0)), bind(X7, $fot(X_119)),
% 3.51/3.71 bind(X_87, $fot(X_120))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_44, plain,
% 3.51/3.71 (add(0, add(X_120, '==>'(X_120, '==>'(0, X_119)))) =
% 3.51/3.71 add(X_120, '==>'(X_120, '==>'(0, X_119)))),
% 3.51/3.71 inference(subst, [],
% 3.51/3.71 [refute_0_15 :
% 3.51/3.71 [bind(A,
% 3.51/3.71 $fot(add(X_120, '==>'(X_120, '==>'(0, X_119)))))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_45, plain,
% 3.51/3.71 (add(0, add(X_120, '==>'(X_120, '==>'(0, X_119)))) !=
% 3.51/3.71 add(X_120, '==>'(X_120, '==>'(0, X_119))) |
% 3.51/3.71 ~
% 3.51/3.71 greater_equal(add(0, add(X_120, '==>'(X_120, '==>'(0, X_119)))),
% 3.51/3.71 X_119) |
% 3.51/3.71 greater_equal(add(X_120, '==>'(X_120, '==>'(0, X_119))), X_119)),
% 3.51/3.71 introduced(tautology,
% 3.51/3.71 [equality,
% 3.51/3.71 [$cnf(greater_equal(add(0,
% 3.51/3.71 add(X_120, '==>'(X_120, '==>'(0, X_119)))),
% 3.51/3.71 X_119)), [0],
% 3.51/3.71 $fot(add(X_120, '==>'(X_120, '==>'(0, X_119))))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_46, plain,
% 3.51/3.71 (~
% 3.51/3.71 greater_equal(add(0, add(X_120, '==>'(X_120, '==>'(0, X_119)))),
% 3.51/3.71 X_119) |
% 3.51/3.71 greater_equal(add(X_120, '==>'(X_120, '==>'(0, X_119))), X_119)),
% 3.51/3.71 inference(resolve,
% 3.51/3.71 [$cnf($equal(add(0,
% 3.51/3.71 add(X_120, '==>'(X_120, '==>'(0, X_119)))),
% 3.51/3.71 add(X_120, '==>'(X_120, '==>'(0, X_119)))))],
% 3.51/3.71 [refute_0_44, refute_0_45])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_47, plain,
% 3.51/3.71 (greater_equal(add(X_120, '==>'(X_120, '==>'(0, X_119))), X_119)),
% 3.51/3.71 inference(resolve,
% 3.51/3.71 [$cnf(greater_equal(add(0,
% 3.51/3.71 add(X_120, '==>'(X_120, '==>'(0, X_119)))),
% 3.51/3.71 X_119))], [refute_0_43, refute_0_46])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_48, plain,
% 3.51/3.71 (greater_equal(add('==>'('==>'('==>'(0, X_121), 1), '==>'(0, X_121)),
% 3.51/3.71 '==>'('==>'('==>'('==>'(0, X_121), 1), '==>'(0, X_121)),
% 3.51/3.71 '==>'(0, X_121))), X_121)),
% 3.51/3.71 inference(subst, [],
% 3.51/3.71 [refute_0_47 :
% 3.51/3.71 [bind(X_119, $fot(X_121)),
% 3.51/3.71 bind(X_120,
% 3.51/3.71 $fot('==>'('==>'('==>'(0, X_121), 1),
% 3.51/3.71 '==>'(0, X_121))))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_49, plain, ('==>'('==>'('==>'(A, 1), A), A) = 0),
% 3.51/3.71 inference(canonicalize, [], [normalize_0_25])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_50, plain,
% 3.51/3.71 ('==>'('==>'('==>'('==>'(0, X_121), 1), '==>'(0, X_121)),
% 3.51/3.71 '==>'(0, X_121)) = 0),
% 3.51/3.71 inference(subst, [],
% 3.51/3.71 [refute_0_49 : [bind(A, $fot('==>'(0, X_121)))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_51, plain,
% 3.51/3.71 ('==>'('==>'('==>'('==>'(0, X_121), 1), '==>'(0, X_121)),
% 3.51/3.71 '==>'(0, X_121)) != 0 |
% 3.51/3.71 ~
% 3.51/3.71 greater_equal(add('==>'('==>'('==>'(0, X_121), 1), '==>'(0, X_121)),
% 3.51/3.71 '==>'('==>'('==>'('==>'(0, X_121), 1), '==>'(0, X_121)),
% 3.51/3.71 '==>'(0, X_121))), X_121) |
% 3.51/3.71 greater_equal(add('==>'('==>'('==>'(0, X_121), 1), '==>'(0, X_121)),
% 3.51/3.71 0), X_121)),
% 3.51/3.71 introduced(tautology,
% 3.51/3.71 [equality,
% 3.51/3.71 [$cnf(greater_equal(add('==>'('==>'('==>'(0, X_121), 1),
% 3.51/3.71 '==>'(0, X_121)),
% 3.51/3.71 '==>'('==>'('==>'('==>'(0, X_121), 1),
% 3.51/3.71 '==>'(0, X_121)), '==>'(0, X_121))), X_121)),
% 3.51/3.71 [0, 1], $fot(0)]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_52, plain,
% 3.51/3.71 (~
% 3.51/3.71 greater_equal(add('==>'('==>'('==>'(0, X_121), 1), '==>'(0, X_121)),
% 3.51/3.71 '==>'('==>'('==>'('==>'(0, X_121), 1), '==>'(0, X_121)),
% 3.51/3.71 '==>'(0, X_121))), X_121) |
% 3.51/3.71 greater_equal(add('==>'('==>'('==>'(0, X_121), 1), '==>'(0, X_121)),
% 3.51/3.71 0), X_121)),
% 3.51/3.71 inference(resolve,
% 3.51/3.71 [$cnf($equal('==>'('==>'('==>'('==>'(0, X_121), 1),
% 3.51/3.71 '==>'(0, X_121)), '==>'(0, X_121)), 0))],
% 3.51/3.71 [refute_0_50, refute_0_51])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_53, plain,
% 3.51/3.71 (greater_equal(add('==>'('==>'('==>'(0, X_121), 1), '==>'(0, X_121)),
% 3.51/3.71 0), X_121)),
% 3.51/3.71 inference(resolve,
% 3.51/3.71 [$cnf(greater_equal(add('==>'('==>'('==>'(0, X_121), 1),
% 3.51/3.71 '==>'(0, X_121)),
% 3.51/3.71 '==>'('==>'('==>'('==>'(0, X_121), 1),
% 3.51/3.71 '==>'(0, X_121)), '==>'(0, X_121))), X_121))],
% 3.51/3.71 [refute_0_48, refute_0_52])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_54, plain,
% 3.51/3.71 (add('==>'('==>'('==>'(0, X_121), 1), '==>'(0, X_121)), 0) =
% 3.51/3.71 '==>'('==>'('==>'(0, X_121), 1), '==>'(0, X_121))),
% 3.51/3.71 inference(subst, [],
% 3.51/3.71 [refute_0_1 :
% 3.51/3.71 [bind(A,
% 3.51/3.71 $fot('==>'('==>'('==>'(0, X_121), 1),
% 3.51/3.71 '==>'(0, X_121))))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_55, plain,
% 3.51/3.71 (add('==>'('==>'('==>'(0, X_121), 1), '==>'(0, X_121)), 0) !=
% 3.51/3.71 '==>'('==>'('==>'(0, X_121), 1), '==>'(0, X_121)) |
% 3.51/3.71 ~
% 3.51/3.71 greater_equal(add('==>'('==>'('==>'(0, X_121), 1), '==>'(0, X_121)),
% 3.51/3.71 0), X_121) |
% 3.51/3.71 greater_equal('==>'('==>'('==>'(0, X_121), 1), '==>'(0, X_121)),
% 3.51/3.71 X_121)),
% 3.51/3.71 introduced(tautology,
% 3.51/3.71 [equality,
% 3.51/3.71 [$cnf(greater_equal(add('==>'('==>'('==>'(0, X_121), 1),
% 3.51/3.71 '==>'(0, X_121)), 0), X_121)), [0],
% 3.51/3.71 $fot('==>'('==>'('==>'(0, X_121), 1),
% 3.51/3.71 '==>'(0, X_121)))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_56, plain,
% 3.51/3.71 (~
% 3.51/3.71 greater_equal(add('==>'('==>'('==>'(0, X_121), 1), '==>'(0, X_121)),
% 3.51/3.71 0), X_121) |
% 3.51/3.71 greater_equal('==>'('==>'('==>'(0, X_121), 1), '==>'(0, X_121)),
% 3.51/3.71 X_121)),
% 3.51/3.71 inference(resolve,
% 3.51/3.71 [$cnf($equal(add('==>'('==>'('==>'(0, X_121), 1),
% 3.51/3.71 '==>'(0, X_121)), 0),
% 3.51/3.71 '==>'('==>'('==>'(0, X_121), 1), '==>'(0, X_121))))],
% 3.51/3.71 [refute_0_54, refute_0_55])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_57, plain,
% 3.51/3.71 (greater_equal('==>'('==>'('==>'(0, X_121), 1), '==>'(0, X_121)),
% 3.51/3.71 X_121)),
% 3.51/3.71 inference(resolve,
% 3.51/3.71 [$cnf(greater_equal(add('==>'('==>'('==>'(0, X_121), 1),
% 3.51/3.71 '==>'(0, X_121)), 0), X_121))],
% 3.51/3.71 [refute_0_53, refute_0_56])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_58, plain,
% 3.51/3.71 (greater_equal('==>'('==>'('==>'(0, X_447), 1), '==>'(0, X_447)),
% 3.51/3.71 X_447)),
% 3.51/3.71 inference(subst, [], [refute_0_57 : [bind(X_121, $fot(X_447))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_59, plain,
% 3.51/3.71 (~
% 3.51/3.71 greater_equal(X_447,
% 3.51/3.71 '==>'('==>'('==>'(0, X_447), 1), '==>'(0, X_447))) |
% 3.51/3.71 ~
% 3.51/3.71 greater_equal('==>'('==>'('==>'(0, X_447), 1), '==>'(0, X_447)),
% 3.51/3.71 X_447) |
% 3.51/3.71 '==>'('==>'('==>'(0, X_447), 1), '==>'(0, X_447)) = X_447),
% 3.51/3.71 inference(subst, [],
% 3.51/3.71 [refute_0_3 :
% 3.51/3.71 [bind(X3,
% 3.51/3.71 $fot('==>'('==>'('==>'(0, X_447), 1),
% 3.51/3.71 '==>'(0, X_447)))), bind(X4, $fot(X_447))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_60, plain,
% 3.51/3.71 (~
% 3.51/3.71 greater_equal(X_447,
% 3.51/3.71 '==>'('==>'('==>'(0, X_447), 1), '==>'(0, X_447))) |
% 3.51/3.71 '==>'('==>'('==>'(0, X_447), 1), '==>'(0, X_447)) = X_447),
% 3.51/3.71 inference(resolve,
% 3.51/3.71 [$cnf(greater_equal('==>'('==>'('==>'(0, X_447), 1),
% 3.51/3.71 '==>'(0, X_447)), X_447))],
% 3.51/3.71 [refute_0_58, refute_0_59])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_61, plain, (greater_equal(add(0, '==>'(0, X_88)), X_88)),
% 3.51/3.71 inference(subst, [],
% 3.51/3.71 [refute_0_40 :
% 3.51/3.71 [bind(X_84, $fot(0)), bind(X_86, $fot(X_88))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_62, plain, (add(0, '==>'(0, X_88)) = '==>'(0, X_88)),
% 3.51/3.71 inference(subst, [], [refute_0_15 : [bind(A, $fot('==>'(0, X_88)))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_63, plain,
% 3.51/3.71 (add(0, '==>'(0, X_88)) != '==>'(0, X_88) |
% 3.51/3.71 ~ greater_equal(add(0, '==>'(0, X_88)), X_88) |
% 3.51/3.71 greater_equal('==>'(0, X_88), X_88)),
% 3.51/3.71 introduced(tautology,
% 3.51/3.71 [equality,
% 3.51/3.71 [$cnf(greater_equal(add(0, '==>'(0, X_88)), X_88)), [0],
% 3.51/3.71 $fot('==>'(0, X_88))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_64, plain,
% 3.51/3.71 (~ greater_equal(add(0, '==>'(0, X_88)), X_88) |
% 3.51/3.71 greater_equal('==>'(0, X_88), X_88)),
% 3.51/3.71 inference(resolve,
% 3.51/3.71 [$cnf($equal(add(0, '==>'(0, X_88)), '==>'(0, X_88)))],
% 3.51/3.71 [refute_0_62, refute_0_63])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_65, plain, (greater_equal('==>'(0, X_88), X_88)),
% 3.51/3.71 inference(resolve, [$cnf(greater_equal(add(0, '==>'(0, X_88)), X_88))],
% 3.51/3.71 [refute_0_61, refute_0_64])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_66, plain, (greater_equal('==>'(0, X_447), X_447)),
% 3.51/3.71 inference(subst, [], [refute_0_65 : [bind(X_88, $fot(X_447))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_67, plain,
% 3.51/3.71 (~ greater_equal(X_447, '==>'(0, X_447)) |
% 3.51/3.71 ~ greater_equal('==>'(0, X_447), X_447) | '==>'(0, X_447) = X_447),
% 3.51/3.71 inference(subst, [],
% 3.51/3.71 [refute_0_3 :
% 3.51/3.71 [bind(X3, $fot('==>'(0, X_447))), bind(X4, $fot(X_447))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_68, plain,
% 3.51/3.71 (~ greater_equal(X_447, '==>'(0, X_447)) | '==>'(0, X_447) = X_447),
% 3.51/3.71 inference(resolve, [$cnf(greater_equal('==>'(0, X_447), X_447))],
% 3.51/3.71 [refute_0_66, refute_0_67])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_69, plain, (greater_equal(add(X_154, X_156), X_156)),
% 3.51/3.71 inference(subst, [],
% 3.51/3.71 [refute_0_19 :
% 3.51/3.71 [bind(X_21, $fot(X_156)), bind(X_22, $fot(X_154))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_70, plain,
% 3.51/3.71 (~ greater_equal(add(X5, X6), X7) | greater_equal(X6, '==>'(X5, X7))),
% 3.51/3.71 inference(canonicalize, [], [normalize_0_26])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_71, plain,
% 3.51/3.71 (~ greater_equal(add(X_154, X_156), X_156) |
% 3.51/3.71 greater_equal(X_156, '==>'(X_154, X_156))),
% 3.51/3.71 inference(subst, [],
% 3.51/3.71 [refute_0_70 :
% 3.51/3.71 [bind(X5, $fot(X_154)), bind(X6, $fot(X_156)),
% 3.51/3.71 bind(X7, $fot(X_156))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_72, plain, (greater_equal(X_156, '==>'(X_154, X_156))),
% 3.51/3.71 inference(resolve, [$cnf(greater_equal(add(X_154, X_156), X_156))],
% 3.51/3.71 [refute_0_69, refute_0_71])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_73, plain, (greater_equal(X_447, '==>'(0, X_447))),
% 3.51/3.71 inference(subst, [],
% 3.51/3.71 [refute_0_72 :
% 3.51/3.71 [bind(X_154, $fot(0)), bind(X_156, $fot(X_447))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_74, plain, ('==>'(0, X_447) = X_447),
% 3.51/3.71 inference(resolve, [$cnf(greater_equal(X_447, '==>'(0, X_447)))],
% 3.51/3.71 [refute_0_73, refute_0_68])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_75, plain,
% 3.51/3.71 ('==>'('==>'(X_447, 1), '==>'(0, X_447)) =
% 3.51/3.71 '==>'('==>'(X_447, 1), '==>'(0, X_447))),
% 3.51/3.71 introduced(tautology,
% 3.51/3.71 [refl, [$fot('==>'('==>'(X_447, 1), '==>'(0, X_447)))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_76, plain,
% 3.51/3.71 ('==>'(0, X_447) != X_447 |
% 3.51/3.71 '==>'('==>'(X_447, 1), '==>'(0, X_447)) !=
% 3.51/3.71 '==>'('==>'(X_447, 1), '==>'(0, X_447)) |
% 3.51/3.71 '==>'('==>'(X_447, 1), '==>'(0, X_447)) =
% 3.51/3.71 '==>'('==>'(X_447, 1), X_447)),
% 3.51/3.71 introduced(tautology,
% 3.51/3.71 [equality,
% 3.51/3.71 [$cnf($equal('==>'('==>'(X_447, 1), '==>'(0, X_447)),
% 3.51/3.71 '==>'('==>'(X_447, 1), '==>'(0, X_447)))), [1, 1],
% 3.51/3.71 $fot(X_447)]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_77, plain,
% 3.51/3.71 ('==>'(0, X_447) != X_447 |
% 3.51/3.71 '==>'('==>'(X_447, 1), '==>'(0, X_447)) =
% 3.51/3.71 '==>'('==>'(X_447, 1), X_447)),
% 3.51/3.71 inference(resolve,
% 3.51/3.71 [$cnf($equal('==>'('==>'(X_447, 1), '==>'(0, X_447)),
% 3.51/3.71 '==>'('==>'(X_447, 1), '==>'(0, X_447))))],
% 3.51/3.71 [refute_0_75, refute_0_76])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_78, plain,
% 3.51/3.71 ('==>'('==>'(X_447, 1), '==>'(0, X_447)) =
% 3.51/3.71 '==>'('==>'(X_447, 1), X_447)),
% 3.51/3.71 inference(resolve, [$cnf($equal('==>'(0, X_447), X_447))],
% 3.51/3.71 [refute_0_74, refute_0_77])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_79, plain,
% 3.51/3.71 ('==>'('==>'(0, X_447), 1) = '==>'('==>'(0, X_447), 1)),
% 3.51/3.71 introduced(tautology, [refl, [$fot('==>'('==>'(0, X_447), 1))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_80, plain,
% 3.51/3.71 ('==>'(0, X_447) != X_447 |
% 3.51/3.71 '==>'('==>'(0, X_447), 1) != '==>'('==>'(0, X_447), 1) |
% 3.51/3.71 '==>'('==>'(0, X_447), 1) = '==>'(X_447, 1)),
% 3.51/3.71 introduced(tautology,
% 3.51/3.71 [equality,
% 3.51/3.71 [$cnf($equal('==>'('==>'(0, X_447), 1),
% 3.51/3.71 '==>'('==>'(0, X_447), 1))), [1, 0],
% 3.51/3.71 $fot(X_447)]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_81, plain,
% 3.51/3.71 ('==>'(0, X_447) != X_447 |
% 3.51/3.71 '==>'('==>'(0, X_447), 1) = '==>'(X_447, 1)),
% 3.51/3.71 inference(resolve,
% 3.51/3.71 [$cnf($equal('==>'('==>'(0, X_447), 1),
% 3.51/3.71 '==>'('==>'(0, X_447), 1)))],
% 3.51/3.71 [refute_0_79, refute_0_80])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_82, plain, ('==>'('==>'(0, X_447), 1) = '==>'(X_447, 1)),
% 3.51/3.71 inference(resolve, [$cnf($equal('==>'(0, X_447), X_447))],
% 3.51/3.71 [refute_0_74, refute_0_81])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_83, plain,
% 3.51/3.71 ('==>'('==>'('==>'(0, X_447), 1), '==>'(0, X_447)) =
% 3.51/3.71 '==>'('==>'('==>'(0, X_447), 1), '==>'(0, X_447))),
% 3.51/3.71 introduced(tautology,
% 3.51/3.71 [refl,
% 3.51/3.71 [$fot('==>'('==>'('==>'(0, X_447), 1),
% 3.51/3.71 '==>'(0, X_447)))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_84, plain,
% 3.51/3.71 ('==>'('==>'(0, X_447), 1) != '==>'(X_447, 1) |
% 3.51/3.71 '==>'('==>'('==>'(0, X_447), 1), '==>'(0, X_447)) !=
% 3.51/3.71 '==>'('==>'('==>'(0, X_447), 1), '==>'(0, X_447)) |
% 3.51/3.71 '==>'('==>'('==>'(0, X_447), 1), '==>'(0, X_447)) =
% 3.51/3.71 '==>'('==>'(X_447, 1), '==>'(0, X_447))),
% 3.51/3.71 introduced(tautology,
% 3.51/3.71 [equality,
% 3.51/3.71 [$cnf($equal('==>'('==>'('==>'(0, X_447), 1),
% 3.51/3.71 '==>'(0, X_447)),
% 3.51/3.71 '==>'('==>'('==>'(0, X_447), 1),
% 3.51/3.71 '==>'(0, X_447)))), [1, 0],
% 3.51/3.71 $fot('==>'(X_447, 1))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_85, plain,
% 3.51/3.71 ('==>'('==>'(0, X_447), 1) != '==>'(X_447, 1) |
% 3.51/3.71 '==>'('==>'('==>'(0, X_447), 1), '==>'(0, X_447)) =
% 3.51/3.71 '==>'('==>'(X_447, 1), '==>'(0, X_447))),
% 3.51/3.71 inference(resolve,
% 3.51/3.71 [$cnf($equal('==>'('==>'('==>'(0, X_447), 1),
% 3.51/3.71 '==>'(0, X_447)),
% 3.51/3.71 '==>'('==>'('==>'(0, X_447), 1), '==>'(0, X_447))))],
% 3.51/3.71 [refute_0_83, refute_0_84])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_86, plain,
% 3.51/3.71 ('==>'('==>'('==>'(0, X_447), 1), '==>'(0, X_447)) =
% 3.51/3.71 '==>'('==>'(X_447, 1), '==>'(0, X_447))),
% 3.51/3.71 inference(resolve,
% 3.51/3.71 [$cnf($equal('==>'('==>'(0, X_447), 1), '==>'(X_447, 1)))],
% 3.51/3.71 [refute_0_82, refute_0_85])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_87, plain, (X = X), introduced(tautology, [refl, [$fot(X)]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_88, plain, (X != X | X != Y | Y = X),
% 3.51/3.71 introduced(tautology, [equality, [$cnf($equal(X, X)), [0], $fot(Y)]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_89, plain, (X != Y | Y = X),
% 3.51/3.71 inference(resolve, [$cnf($equal(X, X))], [refute_0_87, refute_0_88])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_90, plain, (Y != X | Y != Z | X = Z),
% 3.51/3.71 introduced(tautology, [equality, [$cnf($equal(Y, Z)), [0], $fot(X)]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_91, plain, (X != Y | Y != Z | X = Z),
% 3.51/3.71 inference(resolve, [$cnf($equal(Y, X))], [refute_0_89, refute_0_90])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_92, plain,
% 3.51/3.71 ('==>'('==>'(X_447, 1), '==>'(0, X_447)) !=
% 3.51/3.71 '==>'('==>'(X_447, 1), X_447) |
% 3.51/3.71 '==>'('==>'('==>'(0, X_447), 1), '==>'(0, X_447)) !=
% 3.51/3.71 '==>'('==>'(X_447, 1), '==>'(0, X_447)) |
% 3.51/3.71 '==>'('==>'('==>'(0, X_447), 1), '==>'(0, X_447)) =
% 3.51/3.71 '==>'('==>'(X_447, 1), X_447)),
% 3.51/3.71 inference(subst, [],
% 3.51/3.71 [refute_0_91 :
% 3.51/3.71 [bind(X,
% 3.51/3.71 $fot('==>'('==>'('==>'(0, X_447), 1),
% 3.51/3.71 '==>'(0, X_447)))),
% 3.51/3.71 bind(Y, $fot('==>'('==>'(X_447, 1), '==>'(0, X_447)))),
% 3.51/3.71 bind(Z, $fot('==>'('==>'(X_447, 1), X_447)))]])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_93, plain,
% 3.51/3.71 ('==>'('==>'(X_447, 1), '==>'(0, X_447)) !=
% 3.51/3.71 '==>'('==>'(X_447, 1), X_447) |
% 3.51/3.71 '==>'('==>'('==>'(0, X_447), 1), '==>'(0, X_447)) =
% 3.51/3.71 '==>'('==>'(X_447, 1), X_447)),
% 3.51/3.71 inference(resolve,
% 3.51/3.71 [$cnf($equal('==>'('==>'('==>'(0, X_447), 1),
% 3.51/3.71 '==>'(0, X_447)),
% 3.51/3.71 '==>'('==>'(X_447, 1), '==>'(0, X_447))))],
% 3.51/3.71 [refute_0_86, refute_0_92])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_94, plain,
% 3.51/3.71 ('==>'('==>'('==>'(0, X_447), 1), '==>'(0, X_447)) =
% 3.51/3.71 '==>'('==>'(X_447, 1), X_447)),
% 3.51/3.71 inference(resolve,
% 3.51/3.71 [$cnf($equal('==>'('==>'(X_447, 1), '==>'(0, X_447)),
% 3.51/3.71 '==>'('==>'(X_447, 1), X_447)))],
% 3.51/3.71 [refute_0_78, refute_0_93])).
% 3.51/3.71
% 3.51/3.71 cnf(refute_0_95, plain,
% 3.51/3.71 ('==>'('==>'('==>'(0, X_447), 1), '==>'(0, X_447)) !=
% 3.51/3.71 '==>'('==>'(X_447, 1), X_447) |
% 3.51/3.71 ~ greater_equal(X_447, '==>'('==>'(X_447, 1), X_447)) |
% 3.51/3.71 greater_equal(X_447,
% 3.51/3.71 '==>'('==>'('==>'(0, X_447), 1), '==>'(0, X_447)))),
% 3.51/3.71 introduced(tautology,
% 3.51/3.71 [equality,
% 3.51/3.71 [$cnf(~ greater_equal(X_447,
% 3.51/3.71 '==>'('==>'('==>'(0, X_447), 1),
% 3.51/3.71 '==>'(0, X_447)))), [1],
% 3.51/3.71 $fot('==>'('==>'(X_447, 1), X_447))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_96, plain,
% 3.55/3.71 (~ greater_equal(X_447, '==>'('==>'(X_447, 1), X_447)) |
% 3.55/3.71 greater_equal(X_447,
% 3.55/3.71 '==>'('==>'('==>'(0, X_447), 1), '==>'(0, X_447)))),
% 3.55/3.71 inference(resolve,
% 3.55/3.71 [$cnf($equal('==>'('==>'('==>'(0, X_447), 1),
% 3.55/3.71 '==>'(0, X_447)), '==>'('==>'(X_447, 1), X_447)))],
% 3.55/3.71 [refute_0_94, refute_0_95])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_97, plain,
% 3.55/3.71 (~ greater_equal(X_447, '==>'('==>'(X_447, 1), X_447)) |
% 3.55/3.71 '==>'('==>'('==>'(0, X_447), 1), '==>'(0, X_447)) = X_447),
% 3.55/3.71 inference(resolve,
% 3.55/3.71 [$cnf(greater_equal(X_447,
% 3.55/3.71 '==>'('==>'('==>'(0, X_447), 1), '==>'(0, X_447))))],
% 3.55/3.71 [refute_0_96, refute_0_60])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_98, plain,
% 3.55/3.71 ('==>'('==>'('==>'(0, X_447), 1), '==>'(0, X_447)) != X_447 |
% 3.55/3.71 '==>'('==>'('==>'(0, X_447), 1), '==>'(0, X_447)) !=
% 3.55/3.71 '==>'('==>'(X_447, 1), X_447) |
% 3.55/3.71 '==>'('==>'(X_447, 1), X_447) = X_447),
% 3.55/3.71 introduced(tautology,
% 3.55/3.71 [equality,
% 3.55/3.71 [$cnf($equal('==>'('==>'('==>'(0, X_447), 1),
% 3.55/3.71 '==>'(0, X_447)), X_447)), [0],
% 3.55/3.71 $fot('==>'('==>'(X_447, 1), X_447))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_99, plain,
% 3.55/3.71 ('==>'('==>'('==>'(0, X_447), 1), '==>'(0, X_447)) != X_447 |
% 3.55/3.71 '==>'('==>'(X_447, 1), X_447) = X_447),
% 3.55/3.71 inference(resolve,
% 3.55/3.71 [$cnf($equal('==>'('==>'('==>'(0, X_447), 1),
% 3.55/3.71 '==>'(0, X_447)), '==>'('==>'(X_447, 1), X_447)))],
% 3.55/3.71 [refute_0_94, refute_0_98])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_100, plain,
% 3.55/3.71 (~ greater_equal(X_447, '==>'('==>'(X_447, 1), X_447)) |
% 3.55/3.71 '==>'('==>'(X_447, 1), X_447) = X_447),
% 3.55/3.71 inference(resolve,
% 3.55/3.71 [$cnf($equal('==>'('==>'('==>'(0, X_447), 1),
% 3.55/3.71 '==>'(0, X_447)), X_447))],
% 3.55/3.71 [refute_0_97, refute_0_99])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_101, plain,
% 3.55/3.71 (greater_equal(X_447, '==>'('==>'(X_447, 1), X_447))),
% 3.55/3.71 inference(subst, [],
% 3.55/3.71 [refute_0_72 :
% 3.55/3.71 [bind(X_154, $fot('==>'(X_447, 1))),
% 3.55/3.71 bind(X_156, $fot(X_447))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_102, plain, ('==>'('==>'(X_447, 1), X_447) = X_447),
% 3.55/3.71 inference(resolve,
% 3.55/3.71 [$cnf(greater_equal(X_447, '==>'('==>'(X_447, 1), X_447)))],
% 3.55/3.71 [refute_0_101, refute_0_100])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_103, plain, ('==>'('==>'(X_402, 1), X_402) = X_402),
% 3.55/3.71 inference(subst, [], [refute_0_102 : [bind(X_447, $fot(X_402))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_104, plain,
% 3.55/3.71 ('==>'('==>'(X_402, 1), X_402) != X_402 |
% 3.55/3.71 ~
% 3.55/3.71 greater_equal('==>'('==>'(X_402, 1), 1),
% 3.55/3.71 '==>'('==>'(X_402, 1), X_402)) |
% 3.55/3.71 greater_equal('==>'('==>'(X_402, 1), 1), X_402)),
% 3.55/3.71 introduced(tautology,
% 3.55/3.71 [equality,
% 3.55/3.71 [$cnf(greater_equal('==>'('==>'(X_402, 1), 1),
% 3.55/3.71 '==>'('==>'(X_402, 1), X_402))), [1],
% 3.55/3.71 $fot(X_402)]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_105, plain,
% 3.55/3.71 (~
% 3.55/3.71 greater_equal('==>'('==>'(X_402, 1), 1),
% 3.55/3.71 '==>'('==>'(X_402, 1), X_402)) |
% 3.55/3.71 greater_equal('==>'('==>'(X_402, 1), 1), X_402)),
% 3.55/3.71 inference(resolve,
% 3.55/3.71 [$cnf($equal('==>'('==>'(X_402, 1), X_402), X_402))],
% 3.55/3.71 [refute_0_103, refute_0_104])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_106, plain, (greater_equal('==>'('==>'(X_402, 1), 1), X_402)),
% 3.55/3.71 inference(resolve,
% 3.55/3.71 [$cnf(greater_equal('==>'('==>'(X_402, 1), 1),
% 3.55/3.71 '==>'('==>'(X_402, 1), X_402)))],
% 3.55/3.71 [refute_0_34, refute_0_105])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_107, plain, (greater_equal('==>'('==>'(X_451, 1), 1), X_451)),
% 3.55/3.71 inference(subst, [], [refute_0_106 : [bind(X_402, $fot(X_451))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_108, plain,
% 3.55/3.71 (greater_equal(add('==>'('==>'(X_451, 1), 1), X10), add(X_451, X10))),
% 3.55/3.71 inference(resolve,
% 3.55/3.71 [$cnf(greater_equal('==>'('==>'(X_451, 1), 1), X_451))],
% 3.55/3.71 [refute_0_107, refute_0_6])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_109, plain,
% 3.55/3.71 (greater_equal(add('==>'('==>'(X_512, 1), 1), X_511),
% 3.55/3.71 add(X_512, X_511))),
% 3.55/3.71 inference(subst, [],
% 3.55/3.71 [refute_0_108 :
% 3.55/3.71 [bind(X10, $fot(X_511)), bind(X_451, $fot(X_512))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_110, plain,
% 3.55/3.71 (~
% 3.55/3.71 greater_equal(add(X_512, X_511),
% 3.55/3.71 add('==>'('==>'(X_512, 1), 1), X_511)) |
% 3.55/3.71 add(X_512, X_511) = add('==>'('==>'(X_512, 1), 1), X_511)),
% 3.55/3.71 inference(resolve,
% 3.55/3.71 [$cnf(greater_equal(add('==>'('==>'(X_512, 1), 1), X_511),
% 3.55/3.71 add(X_512, X_511)))], [refute_0_109, refute_0_4])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_111, plain,
% 3.55/3.71 (~ greater_equal(X_468, '==>'('==>'(X_468, 1), 1)) |
% 3.55/3.71 greater_equal(add(X_468, X10), add('==>'('==>'(X_468, 1), 1), X10))),
% 3.55/3.71 inference(subst, [],
% 3.55/3.71 [refute_0_5 :
% 3.55/3.71 [bind(X8, $fot(X_468)),
% 3.55/3.71 bind(X9, $fot('==>'('==>'(X_468, 1), 1)))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_112, plain,
% 3.55/3.71 (greater_equal(add(X_25, add(X_11, X_10)), add(X_11, X_10))),
% 3.55/3.71 inference(subst, [],
% 3.55/3.71 [refute_0_19 :
% 3.55/3.71 [bind(X_21, $fot(add(X_11, X_10))),
% 3.55/3.71 bind(X_22, $fot(X_25))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_113, plain, (add(add(A, B), C) = add(A, add(B, C))),
% 3.55/3.71 inference(canonicalize, [], [normalize_0_28])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_114, plain,
% 3.55/3.71 (add(add(X_9, X_10), X_11) = add(X_9, add(X_10, X_11))),
% 3.55/3.71 inference(subst, [],
% 3.55/3.71 [refute_0_113 :
% 3.55/3.71 [bind(A, $fot(X_9)), bind(B, $fot(X_10)),
% 3.55/3.71 bind(C, $fot(X_11))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_115, plain, (add(X_11, X_10) = add(X_10, X_11)),
% 3.55/3.71 inference(subst, [],
% 3.55/3.71 [refute_0_11 : [bind(A, $fot(X_11)), bind(B, $fot(X_10))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_116, plain,
% 3.55/3.71 (add(X_11, X_10) != add(X_10, X_11) |
% 3.55/3.71 add(X_10, X_11) = add(X_11, X_10)),
% 3.55/3.71 inference(subst, [],
% 3.55/3.71 [refute_0_89 :
% 3.55/3.71 [bind(X, $fot(add(X_11, X_10))),
% 3.55/3.71 bind(Y, $fot(add(X_10, X_11)))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_117, plain, (add(X_10, X_11) = add(X_11, X_10)),
% 3.55/3.71 inference(resolve, [$cnf($equal(add(X_11, X_10), add(X_10, X_11)))],
% 3.55/3.71 [refute_0_115, refute_0_116])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_118, plain,
% 3.55/3.71 (add(X_10, X_11) != add(X_11, X_10) |
% 3.55/3.71 add(add(X_9, X_10), X_11) != add(X_9, add(X_10, X_11)) |
% 3.55/3.71 add(add(X_9, X_10), X_11) = add(X_9, add(X_11, X_10))),
% 3.55/3.71 introduced(tautology,
% 3.55/3.71 [equality,
% 3.55/3.71 [$cnf($equal(add(add(X_9, X_10), X_11),
% 3.55/3.71 add(X_9, add(X_10, X_11)))), [1, 1],
% 3.55/3.71 $fot(add(X_11, X_10))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_119, plain,
% 3.55/3.71 (add(add(X_9, X_10), X_11) != add(X_9, add(X_10, X_11)) |
% 3.55/3.71 add(add(X_9, X_10), X_11) = add(X_9, add(X_11, X_10))),
% 3.55/3.71 inference(resolve, [$cnf($equal(add(X_10, X_11), add(X_11, X_10)))],
% 3.55/3.71 [refute_0_117, refute_0_118])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_120, plain,
% 3.55/3.71 (add(add(X_9, X_10), X_11) = add(X_9, add(X_11, X_10))),
% 3.55/3.71 inference(resolve,
% 3.55/3.71 [$cnf($equal(add(add(X_9, X_10), X_11),
% 3.55/3.71 add(X_9, add(X_10, X_11))))],
% 3.55/3.71 [refute_0_114, refute_0_119])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_121, plain,
% 3.55/3.71 (add(add(X_9, X_10), X_11) != add(X_9, add(X_10, X_11)) |
% 3.55/3.71 add(add(X_9, X_10), X_11) != add(X_9, add(X_11, X_10)) |
% 3.55/3.71 add(X_9, add(X_10, X_11)) = add(X_9, add(X_11, X_10))),
% 3.55/3.71 introduced(tautology,
% 3.55/3.71 [equality,
% 3.55/3.71 [$cnf($equal(add(add(X_9, X_10), X_11),
% 3.55/3.71 add(X_9, add(X_11, X_10)))), [0],
% 3.55/3.71 $fot(add(X_9, add(X_10, X_11)))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_122, plain,
% 3.55/3.71 (add(add(X_9, X_10), X_11) != add(X_9, add(X_11, X_10)) |
% 3.55/3.71 add(X_9, add(X_10, X_11)) = add(X_9, add(X_11, X_10))),
% 3.55/3.71 inference(resolve,
% 3.55/3.71 [$cnf($equal(add(add(X_9, X_10), X_11),
% 3.55/3.71 add(X_9, add(X_10, X_11))))],
% 3.55/3.71 [refute_0_114, refute_0_121])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_123, plain,
% 3.55/3.71 (add(X_9, add(X_10, X_11)) = add(X_9, add(X_11, X_10))),
% 3.55/3.71 inference(resolve,
% 3.55/3.71 [$cnf($equal(add(add(X_9, X_10), X_11),
% 3.55/3.71 add(X_9, add(X_11, X_10))))],
% 3.55/3.71 [refute_0_120, refute_0_122])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_124, plain,
% 3.55/3.71 (add(X_25, add(X_10, X_11)) = add(X_25, add(X_11, X_10))),
% 3.55/3.71 inference(subst, [], [refute_0_123 : [bind(X_9, $fot(X_25))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_125, plain,
% 3.55/3.71 (add(X_25, add(X_10, X_11)) != add(X_25, add(X_11, X_10)) |
% 3.55/3.71 add(X_25, add(X_11, X_10)) = add(X_25, add(X_10, X_11))),
% 3.55/3.71 inference(subst, [],
% 3.55/3.71 [refute_0_89 :
% 3.55/3.71 [bind(X, $fot(add(X_25, add(X_10, X_11)))),
% 3.55/3.71 bind(Y, $fot(add(X_25, add(X_11, X_10))))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_126, plain,
% 3.55/3.71 (add(X_25, add(X_11, X_10)) = add(X_25, add(X_10, X_11))),
% 3.55/3.71 inference(resolve,
% 3.55/3.71 [$cnf($equal(add(X_25, add(X_10, X_11)),
% 3.55/3.71 add(X_25, add(X_11, X_10))))],
% 3.55/3.71 [refute_0_124, refute_0_125])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_127, plain,
% 3.55/3.71 (add(X_25, add(X_11, X_10)) != add(X_25, add(X_10, X_11)) |
% 3.55/3.71 ~ greater_equal(add(X_25, add(X_11, X_10)), add(X_11, X_10)) |
% 3.55/3.71 greater_equal(add(X_25, add(X_10, X_11)), add(X_11, X_10))),
% 3.55/3.71 introduced(tautology,
% 3.55/3.71 [equality,
% 3.55/3.71 [$cnf(greater_equal(add(X_25, add(X_11, X_10)),
% 3.55/3.71 add(X_11, X_10))), [0],
% 3.55/3.71 $fot(add(X_25, add(X_10, X_11)))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_128, plain,
% 3.55/3.71 (~ greater_equal(add(X_25, add(X_11, X_10)), add(X_11, X_10)) |
% 3.55/3.71 greater_equal(add(X_25, add(X_10, X_11)), add(X_11, X_10))),
% 3.55/3.71 inference(resolve,
% 3.55/3.71 [$cnf($equal(add(X_25, add(X_11, X_10)),
% 3.55/3.71 add(X_25, add(X_10, X_11))))],
% 3.55/3.71 [refute_0_126, refute_0_127])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_129, plain,
% 3.55/3.71 (greater_equal(add(X_25, add(X_10, X_11)), add(X_11, X_10))),
% 3.55/3.71 inference(resolve,
% 3.55/3.71 [$cnf(greater_equal(add(X_25, add(X_11, X_10)),
% 3.55/3.71 add(X_11, X_10)))], [refute_0_112, refute_0_128])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_130, plain,
% 3.55/3.71 (greater_equal(add(0, add(X_39, X_40)), add(X_40, X_39))),
% 3.55/3.71 inference(subst, [],
% 3.55/3.71 [refute_0_129 :
% 3.55/3.71 [bind(X_10, $fot(X_39)), bind(X_11, $fot(X_40)),
% 3.55/3.71 bind(X_25, $fot(0))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_131, plain, (add(0, add(X_39, X_40)) = add(X_39, X_40)),
% 3.55/3.71 inference(subst, [],
% 3.55/3.71 [refute_0_15 : [bind(A, $fot(add(X_39, X_40)))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_132, plain,
% 3.55/3.71 (add(0, add(X_39, X_40)) != add(X_39, X_40) |
% 3.55/3.71 ~ greater_equal(add(0, add(X_39, X_40)), add(X_40, X_39)) |
% 3.55/3.71 greater_equal(add(X_39, X_40), add(X_40, X_39))),
% 3.55/3.71 introduced(tautology,
% 3.55/3.71 [equality,
% 3.55/3.71 [$cnf(greater_equal(add(0, add(X_39, X_40)),
% 3.55/3.71 add(X_40, X_39))), [0], $fot(add(X_39, X_40))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_133, plain,
% 3.55/3.71 (~ greater_equal(add(0, add(X_39, X_40)), add(X_40, X_39)) |
% 3.55/3.71 greater_equal(add(X_39, X_40), add(X_40, X_39))),
% 3.55/3.71 inference(resolve,
% 3.55/3.71 [$cnf($equal(add(0, add(X_39, X_40)), add(X_39, X_40)))],
% 3.55/3.71 [refute_0_131, refute_0_132])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_134, plain, (greater_equal(add(X_39, X_40), add(X_40, X_39))),
% 3.55/3.71 inference(resolve,
% 3.55/3.71 [$cnf(greater_equal(add(0, add(X_39, X_40)),
% 3.55/3.71 add(X_40, X_39)))], [refute_0_130, refute_0_133])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_135, plain,
% 3.55/3.71 (greater_equal(add(X_154, X_155), add(X_155, X_154))),
% 3.55/3.71 inference(subst, [],
% 3.55/3.71 [refute_0_134 :
% 3.55/3.71 [bind(X_39, $fot(X_154)), bind(X_40, $fot(X_155))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_136, plain,
% 3.55/3.71 (~ greater_equal(add(X_154, X_155), add(X_155, X_154)) |
% 3.55/3.71 greater_equal(X_155, '==>'(X_154, add(X_155, X_154)))),
% 3.55/3.71 inference(subst, [],
% 3.55/3.71 [refute_0_70 :
% 3.55/3.71 [bind(X5, $fot(X_154)), bind(X6, $fot(X_155)),
% 3.55/3.71 bind(X7, $fot(add(X_155, X_154)))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_137, plain,
% 3.55/3.71 (greater_equal(X_155, '==>'(X_154, add(X_155, X_154)))),
% 3.55/3.71 inference(resolve,
% 3.55/3.71 [$cnf(greater_equal(add(X_154, X_155), add(X_155, X_154)))],
% 3.55/3.71 [refute_0_135, refute_0_136])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_138, plain,
% 3.55/3.71 (greater_equal(X_155,
% 3.55/3.71 '==>'('==>'(X_155, 1), add(X_155, '==>'(X_155, 1))))),
% 3.55/3.71 inference(subst, [],
% 3.55/3.71 [refute_0_137 : [bind(X_154, $fot('==>'(X_155, 1)))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_139, plain,
% 3.55/3.71 (~ greater_equal('==>'(X_405, 1), '==>'(X_405, X_404)) |
% 3.55/3.71 greater_equal(add(X_405, '==>'(X_405, 1)), X_404)),
% 3.55/3.71 inference(subst, [],
% 3.55/3.71 [refute_0_35 :
% 3.55/3.71 [bind(X5, $fot(X_405)), bind(X6, $fot('==>'(X_405, 1))),
% 3.55/3.71 bind(X7, $fot(X_404))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_140, plain,
% 3.55/3.71 (greater_equal('==>'(X_405, 1), '==>'(X_405, X_404))),
% 3.55/3.71 inference(subst, [],
% 3.55/3.71 [refute_0_33 :
% 3.55/3.71 [bind(X_402, $fot(X_404)), bind(X_403, $fot(X_405))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_141, plain,
% 3.55/3.71 (greater_equal(add(X_405, '==>'(X_405, 1)), X_404)),
% 3.55/3.71 inference(resolve,
% 3.55/3.71 [$cnf(greater_equal('==>'(X_405, 1), '==>'(X_405, X_404)))],
% 3.55/3.71 [refute_0_140, refute_0_139])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_142, plain, (greater_equal(add(X_405, '==>'(X_405, 1)), 1)),
% 3.55/3.71 inference(subst, [], [refute_0_141 : [bind(X_404, $fot(1))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_143, plain, (greater_equal(1, X_447)),
% 3.55/3.71 inference(subst, [], [refute_0_29 : [bind(X_24, $fot(X_447))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_144, plain,
% 3.55/3.71 (~ greater_equal(X_447, 1) | ~ greater_equal(1, X_447) | 1 = X_447),
% 3.55/3.71 inference(subst, [],
% 3.55/3.71 [refute_0_3 : [bind(X3, $fot(1)), bind(X4, $fot(X_447))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_145, plain, (~ greater_equal(X_447, 1) | 1 = X_447),
% 3.55/3.71 inference(resolve, [$cnf(greater_equal(1, X_447))],
% 3.55/3.71 [refute_0_143, refute_0_144])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_146, plain,
% 3.55/3.71 (~ greater_equal(add(X_405, '==>'(X_405, 1)), 1) |
% 3.55/3.71 1 = add(X_405, '==>'(X_405, 1))),
% 3.55/3.71 inference(subst, [],
% 3.55/3.71 [refute_0_145 :
% 3.55/3.71 [bind(X_447, $fot(add(X_405, '==>'(X_405, 1))))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_147, plain, (1 = add(X_405, '==>'(X_405, 1))),
% 3.55/3.71 inference(resolve,
% 3.55/3.71 [$cnf(greater_equal(add(X_405, '==>'(X_405, 1)), 1))],
% 3.55/3.71 [refute_0_142, refute_0_146])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_148, plain, (1 = add(X_155, '==>'(X_155, 1))),
% 3.55/3.71 inference(subst, [], [refute_0_147 : [bind(X_405, $fot(X_155))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_149, plain,
% 3.55/3.71 (1 != add(X_155, '==>'(X_155, 1)) | add(X_155, '==>'(X_155, 1)) = 1),
% 3.55/3.71 inference(subst, [],
% 3.55/3.71 [refute_0_89 :
% 3.55/3.71 [bind(X, $fot(1)),
% 3.55/3.71 bind(Y, $fot(add(X_155, '==>'(X_155, 1))))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_150, plain, (add(X_155, '==>'(X_155, 1)) = 1),
% 3.55/3.71 inference(resolve, [$cnf($equal(1, add(X_155, '==>'(X_155, 1))))],
% 3.55/3.71 [refute_0_148, refute_0_149])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_151, plain,
% 3.55/3.71 (add(X_155, '==>'(X_155, 1)) != 1 |
% 3.55/3.71 ~
% 3.55/3.71 greater_equal(X_155,
% 3.55/3.71 '==>'('==>'(X_155, 1), add(X_155, '==>'(X_155, 1)))) |
% 3.55/3.71 greater_equal(X_155, '==>'('==>'(X_155, 1), 1))),
% 3.55/3.71 introduced(tautology,
% 3.55/3.71 [equality,
% 3.55/3.71 [$cnf(greater_equal(X_155,
% 3.55/3.71 '==>'('==>'(X_155, 1),
% 3.55/3.71 add(X_155, '==>'(X_155, 1))))), [1, 1],
% 3.55/3.71 $fot(1)]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_152, plain,
% 3.55/3.71 (~
% 3.55/3.71 greater_equal(X_155,
% 3.55/3.71 '==>'('==>'(X_155, 1), add(X_155, '==>'(X_155, 1)))) |
% 3.55/3.71 greater_equal(X_155, '==>'('==>'(X_155, 1), 1))),
% 3.55/3.71 inference(resolve, [$cnf($equal(add(X_155, '==>'(X_155, 1)), 1))],
% 3.55/3.71 [refute_0_150, refute_0_151])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_153, plain, (greater_equal(X_155, '==>'('==>'(X_155, 1), 1))),
% 3.55/3.71 inference(resolve,
% 3.55/3.71 [$cnf(greater_equal(X_155,
% 3.55/3.71 '==>'('==>'(X_155, 1),
% 3.55/3.71 add(X_155, '==>'(X_155, 1)))))],
% 3.55/3.71 [refute_0_138, refute_0_152])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_154, plain, (greater_equal(X_468, '==>'('==>'(X_468, 1), 1))),
% 3.55/3.71 inference(subst, [], [refute_0_153 : [bind(X_155, $fot(X_468))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_155, plain,
% 3.55/3.71 (greater_equal(add(X_468, X10), add('==>'('==>'(X_468, 1), 1), X10))),
% 3.55/3.71 inference(resolve,
% 3.55/3.71 [$cnf(greater_equal(X_468, '==>'('==>'(X_468, 1), 1)))],
% 3.55/3.71 [refute_0_154, refute_0_111])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_156, plain,
% 3.55/3.71 (greater_equal(add(X_512, X_511),
% 3.55/3.71 add('==>'('==>'(X_512, 1), 1), X_511))),
% 3.55/3.71 inference(subst, [],
% 3.55/3.71 [refute_0_155 :
% 3.55/3.71 [bind(X10, $fot(X_511)), bind(X_468, $fot(X_512))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_157, plain,
% 3.55/3.71 (add(X_512, X_511) = add('==>'('==>'(X_512, 1), 1), X_511)),
% 3.55/3.71 inference(resolve,
% 3.55/3.71 [$cnf(greater_equal(add(X_512, X_511),
% 3.55/3.71 add('==>'('==>'(X_512, 1), 1), X_511)))],
% 3.55/3.71 [refute_0_156, refute_0_110])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_158, plain,
% 3.55/3.71 (add(X_628, 0) = add('==>'('==>'(X_628, 1), 1), 0)),
% 3.55/3.71 inference(subst, [],
% 3.55/3.71 [refute_0_157 :
% 3.55/3.71 [bind(X_511, $fot(0)), bind(X_512, $fot(X_628))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_159, plain,
% 3.55/3.71 (add(X_628, 0) != add('==>'('==>'(X_628, 1), 1), 0) |
% 3.55/3.71 add('==>'('==>'(X_628, 1), 1), 0) = add(X_628, 0)),
% 3.55/3.71 inference(subst, [],
% 3.55/3.71 [refute_0_89 :
% 3.55/3.71 [bind(X, $fot(add(X_628, 0))),
% 3.55/3.71 bind(Y, $fot(add('==>'('==>'(X_628, 1), 1), 0)))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_160, plain,
% 3.55/3.71 (add('==>'('==>'(X_628, 1), 1), 0) = add(X_628, 0)),
% 3.55/3.71 inference(resolve,
% 3.55/3.71 [$cnf($equal(add(X_628, 0),
% 3.55/3.71 add('==>'('==>'(X_628, 1), 1), 0)))],
% 3.55/3.71 [refute_0_158, refute_0_159])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_161, plain,
% 3.55/3.71 (add('==>'('==>'(X_628, 1), 1), 0) != add(X_628, 0) |
% 3.55/3.71 add('==>'('==>'(X_628, 1), 1), 0) != '==>'('==>'(X_628, 1), 1) |
% 3.55/3.71 add(X_628, 0) = '==>'('==>'(X_628, 1), 1)),
% 3.55/3.71 introduced(tautology,
% 3.55/3.71 [equality,
% 3.55/3.71 [$cnf($equal(add('==>'('==>'(X_628, 1), 1), 0),
% 3.55/3.71 '==>'('==>'(X_628, 1), 1))), [0],
% 3.55/3.71 $fot(add(X_628, 0))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_162, plain,
% 3.55/3.71 (add('==>'('==>'(X_628, 1), 1), 0) != '==>'('==>'(X_628, 1), 1) |
% 3.55/3.71 add(X_628, 0) = '==>'('==>'(X_628, 1), 1)),
% 3.55/3.71 inference(resolve,
% 3.55/3.71 [$cnf($equal(add('==>'('==>'(X_628, 1), 1), 0),
% 3.55/3.71 add(X_628, 0)))], [refute_0_160, refute_0_161])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_163, plain, (add(X_628, 0) = '==>'('==>'(X_628, 1), 1)),
% 3.55/3.71 inference(resolve,
% 3.55/3.71 [$cnf($equal(add('==>'('==>'(X_628, 1), 1), 0),
% 3.55/3.71 '==>'('==>'(X_628, 1), 1)))],
% 3.55/3.71 [refute_0_2, refute_0_162])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_164, plain, (add(X_628, 0) = X_628),
% 3.55/3.71 inference(subst, [], [refute_0_1 : [bind(A, $fot(X_628))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_165, plain,
% 3.55/3.71 (add(X_628, 0) != X_628 | add(X_628, 0) != '==>'('==>'(X_628, 1), 1) |
% 3.55/3.71 X_628 = '==>'('==>'(X_628, 1), 1)),
% 3.55/3.71 introduced(tautology,
% 3.55/3.71 [equality,
% 3.55/3.71 [$cnf($equal(add(X_628, 0), '==>'('==>'(X_628, 1), 1))),
% 3.55/3.71 [0], $fot(X_628)]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_166, plain,
% 3.55/3.71 (add(X_628, 0) != '==>'('==>'(X_628, 1), 1) |
% 3.55/3.71 X_628 = '==>'('==>'(X_628, 1), 1)),
% 3.55/3.71 inference(resolve, [$cnf($equal(add(X_628, 0), X_628))],
% 3.55/3.71 [refute_0_164, refute_0_165])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_167, plain, (X_628 = '==>'('==>'(X_628, 1), 1)),
% 3.55/3.71 inference(resolve,
% 3.55/3.71 [$cnf($equal(add(X_628, 0), '==>'('==>'(X_628, 1), 1)))],
% 3.55/3.71 [refute_0_163, refute_0_166])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_168, plain,
% 3.55/3.71 (X_628 != '==>'('==>'(X_628, 1), 1) |
% 3.55/3.71 '==>'('==>'(X_628, 1), 1) = X_628),
% 3.55/3.71 inference(subst, [],
% 3.55/3.71 [refute_0_89 :
% 3.55/3.71 [bind(X, $fot(X_628)),
% 3.55/3.71 bind(Y, $fot('==>'('==>'(X_628, 1), 1)))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_169, plain, ('==>'('==>'(X_628, 1), 1) = X_628),
% 3.55/3.71 inference(resolve, [$cnf($equal(X_628, '==>'('==>'(X_628, 1), 1)))],
% 3.55/3.71 [refute_0_167, refute_0_168])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_170, plain,
% 3.55/3.71 ('==>'('==>'(skolemFOFtoCNF_X17, 1), 1) = skolemFOFtoCNF_X17),
% 3.55/3.71 inference(subst, [],
% 3.55/3.71 [refute_0_169 : [bind(X_628, $fot(skolemFOFtoCNF_X17))]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_171, plain,
% 3.55/3.71 ('==>'('==>'(skolemFOFtoCNF_X17, 1), 1) != skolemFOFtoCNF_X17 |
% 3.55/3.71 skolemFOFtoCNF_X17 != skolemFOFtoCNF_X17 |
% 3.55/3.71 '==>'('==>'(skolemFOFtoCNF_X17, 1), 1) = skolemFOFtoCNF_X17),
% 3.55/3.71 introduced(tautology,
% 3.55/3.71 [equality,
% 3.55/3.71 [$cnf(~ $equal('==>'('==>'(skolemFOFtoCNF_X17, 1), 1),
% 3.55/3.71 skolemFOFtoCNF_X17)), [0],
% 3.55/3.71 $fot(skolemFOFtoCNF_X17)]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_172, plain,
% 3.55/3.71 (skolemFOFtoCNF_X17 != skolemFOFtoCNF_X17 |
% 3.55/3.71 '==>'('==>'(skolemFOFtoCNF_X17, 1), 1) = skolemFOFtoCNF_X17),
% 3.55/3.71 inference(resolve,
% 3.55/3.71 [$cnf($equal('==>'('==>'(skolemFOFtoCNF_X17, 1), 1),
% 3.55/3.71 skolemFOFtoCNF_X17))],
% 3.55/3.71 [refute_0_170, refute_0_171])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_173, plain, (skolemFOFtoCNF_X17 != skolemFOFtoCNF_X17),
% 3.55/3.71 inference(resolve,
% 3.55/3.71 [$cnf($equal('==>'('==>'(skolemFOFtoCNF_X17, 1), 1),
% 3.55/3.71 skolemFOFtoCNF_X17))], [refute_0_172, refute_0_0])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_174, plain, (skolemFOFtoCNF_X17 = skolemFOFtoCNF_X17),
% 3.55/3.71 introduced(tautology, [refl, [$fot(skolemFOFtoCNF_X17)]])).
% 3.55/3.71
% 3.55/3.71 cnf(refute_0_175, plain, ($false),
% 3.55/3.71 inference(resolve,
% 3.55/3.71 [$cnf($equal(skolemFOFtoCNF_X17, skolemFOFtoCNF_X17))],
% 3.55/3.71 [refute_0_174, refute_0_173])).
% 3.55/3.71 % SZS output end CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.55/3.71
%------------------------------------------------------------------------------