TSTP Solution File: SYN417+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SYN417+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Aug 22 11:10:48 EDT 2023
% Result : Theorem 3.87s 2.03s
% Output : CNFRefutation 4.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 202 ( 69 unt; 6 typ; 0 def)
% Number of atoms : 355 ( 333 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 348 ( 189 ~; 154 |; 2 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-1 aty)
% Number of variables : 103 (; 101 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ #nlpp > g > f > #skF_2 > #skF_4 > #skF_3 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff(f,type,
f: $i > $i ).
tff(g,type,
g: $i > $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(f_41,negated_conjecture,
~ ( ? [X] :
( ( X = f(g(X)) )
& ! [Y] :
( ( Y = f(g(Y)) )
=> ( X = Y ) ) )
<=> ? [X] :
( ( X = g(f(X)) )
& ! [Y] :
( ( Y = g(f(Y)) )
=> ( X = Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cute) ).
tff(c_28,plain,
( ( f(g('#skF_1')) = '#skF_1' )
| ( g(f('#skF_3')) = '#skF_3' ) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_33,plain,
g(f('#skF_3')) = '#skF_3',
inference(splitLeft,[status(thm)],[c_28]) ).
tff(c_20,plain,
! [Y_6] :
( ( f(g('#skF_1')) = '#skF_1' )
| ( Y_6 = '#skF_3' )
| ( g(f(Y_6)) != Y_6 ) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_39,plain,
f(g('#skF_1')) = '#skF_1',
inference(splitLeft,[status(thm)],[c_20]) ).
tff(c_18,plain,
! [Y_2,Y_6] :
( ( Y_2 = '#skF_1' )
| ( f(g(Y_2)) != Y_2 )
| ( Y_6 = '#skF_3' )
| ( g(f(Y_6)) != Y_6 ) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_47,plain,
! [Y_9] :
( ( Y_9 = '#skF_3' )
| ( g(f(Y_9)) != Y_9 ) ),
inference(splitLeft,[status(thm)],[c_18]) ).
tff(c_54,plain,
g('#skF_1') = '#skF_3',
inference(superposition,[status(thm),theory(equality)],[c_39,c_47]) ).
tff(c_57,plain,
f('#skF_3') = '#skF_1',
inference(demodulation,[status(thm),theory(equality)],[c_54,c_39]) ).
tff(c_6,plain,
! [X_3,X_7] :
( ( '#skF_2'(X_3) != X_3 )
| ( g(f(X_3)) != X_3 )
| ( '#skF_4'(X_7) != X_7 )
| ( f(g(X_7)) != X_7 ) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_282,plain,
! [X_25] :
( ( '#skF_4'(X_25) != X_25 )
| ( f(g(X_25)) != X_25 ) ),
inference(splitLeft,[status(thm)],[c_6]) ).
tff(c_285,plain,
( ( '#skF_4'('#skF_1') != '#skF_1' )
| ( f('#skF_3') != '#skF_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_54,c_282]) ).
tff(c_287,plain,
'#skF_4'('#skF_1') != '#skF_1',
inference(demodulation,[status(thm),theory(equality)],[c_57,c_285]) ).
tff(c_14,plain,
! [X_3,X_7] :
( ( '#skF_2'(X_3) != X_3 )
| ( g(f(X_3)) != X_3 )
| ( f(g('#skF_4'(X_7))) = '#skF_4'(X_7) )
| ( f(g(X_7)) != X_7 ) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_289,plain,
! [X_26] :
( ( '#skF_2'(X_26) != X_26 )
| ( g(f(X_26)) != X_26 ) ),
inference(splitLeft,[status(thm)],[c_14]) ).
tff(c_292,plain,
( ( '#skF_2'('#skF_3') != '#skF_3' )
| ( g('#skF_1') != '#skF_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_57,c_289]) ).
tff(c_294,plain,
'#skF_2'('#skF_3') != '#skF_3',
inference(demodulation,[status(thm),theory(equality)],[c_54,c_292]) ).
tff(c_16,plain,
! [X_3,X_7] :
( ( g(f('#skF_2'(X_3))) = '#skF_2'(X_3) )
| ( g(f(X_3)) != X_3 )
| ( f(g('#skF_4'(X_7))) = '#skF_4'(X_7) )
| ( f(g(X_7)) != X_7 ) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_296,plain,
! [X_27] :
( ( f(g('#skF_4'(X_27))) = '#skF_4'(X_27) )
| ( f(g(X_27)) != X_27 ) ),
inference(splitLeft,[status(thm)],[c_16]) ).
tff(c_2,plain,
! [Y_2,X_7] :
( ( Y_2 = '#skF_1' )
| ( f(g(Y_2)) != Y_2 )
| ( '#skF_4'(X_7) != X_7 )
| ( f(g(X_7)) != X_7 ) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_75,plain,
! [X_10] :
( ( '#skF_4'(X_10) != X_10 )
| ( f(g(X_10)) != X_10 ) ),
inference(splitLeft,[status(thm)],[c_2]) ).
tff(c_78,plain,
( ( '#skF_4'('#skF_1') != '#skF_1' )
| ( f('#skF_3') != '#skF_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_54,c_75]) ).
tff(c_80,plain,
'#skF_4'('#skF_1') != '#skF_1',
inference(demodulation,[status(thm),theory(equality)],[c_57,c_78]) ).
tff(c_155,plain,
! [X_17] :
( ( '#skF_2'(X_17) != X_17 )
| ( g(f(X_17)) != X_17 ) ),
inference(splitLeft,[status(thm)],[c_14]) ).
tff(c_158,plain,
( ( '#skF_2'('#skF_3') != '#skF_3' )
| ( g('#skF_1') != '#skF_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_57,c_155]) ).
tff(c_160,plain,
'#skF_2'('#skF_3') != '#skF_3',
inference(demodulation,[status(thm),theory(equality)],[c_54,c_158]) ).
tff(c_162,plain,
! [X_18] :
( ( f(g('#skF_4'(X_18))) = '#skF_4'(X_18) )
| ( f(g(X_18)) != X_18 ) ),
inference(splitLeft,[status(thm)],[c_16]) ).
tff(c_10,plain,
! [Y_2,X_7] :
( ( Y_2 = '#skF_1' )
| ( f(g(Y_2)) != Y_2 )
| ( f(g('#skF_4'(X_7))) = '#skF_4'(X_7) )
| ( f(g(X_7)) != X_7 ) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_84,plain,
! [X_11] :
( ( f(g('#skF_4'(X_11))) = '#skF_4'(X_11) )
| ( f(g(X_11)) != X_11 ) ),
inference(splitLeft,[status(thm)],[c_10]) ).
tff(c_46,plain,
! [Y_6] :
( ( Y_6 = '#skF_3' )
| ( g(f(Y_6)) != Y_6 ) ),
inference(splitLeft,[status(thm)],[c_18]) ).
tff(c_101,plain,
! [X_12] :
( ( g('#skF_4'(X_12)) = '#skF_3' )
| ( f(g(X_12)) != X_12 ) ),
inference(superposition,[status(thm),theory(equality)],[c_84,c_46]) ).
tff(c_83,plain,
! [X_7] :
( ( f(g('#skF_4'(X_7))) = '#skF_4'(X_7) )
| ( f(g(X_7)) != X_7 ) ),
inference(splitLeft,[status(thm)],[c_10]) ).
tff(c_107,plain,
! [X_12] :
( ( f('#skF_3') = '#skF_4'(X_12) )
| ( f(g(X_12)) != X_12 )
| ( f(g(X_12)) != X_12 ) ),
inference(superposition,[status(thm),theory(equality)],[c_101,c_83]) ).
tff(c_133,plain,
! [X_15] :
( ( '#skF_4'(X_15) = '#skF_1' )
| ( f(g(X_15)) != X_15 )
| ( f(g(X_15)) != X_15 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_57,c_107]) ).
tff(c_139,plain,
( ( '#skF_4'('#skF_1') = '#skF_1' )
| ( f('#skF_3') != '#skF_1' )
| ( f(g('#skF_1')) != '#skF_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_54,c_133]) ).
tff(c_143,plain,
'#skF_4'('#skF_1') = '#skF_1',
inference(demodulation,[status(thm),theory(equality)],[c_57,c_54,c_57,c_139]) ).
tff(c_145,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_80,c_143]) ).
tff(c_146,plain,
! [Y_2] :
( ( Y_2 = '#skF_1' )
| ( f(g(Y_2)) != Y_2 ) ),
inference(splitRight,[status(thm)],[c_10]) ).
tff(c_187,plain,
! [X_19] :
( ( '#skF_4'(X_19) = '#skF_1' )
| ( f(g(X_19)) != X_19 ) ),
inference(superposition,[status(thm),theory(equality)],[c_162,c_146]) ).
tff(c_193,plain,
( ( '#skF_4'('#skF_1') = '#skF_1' )
| ( f('#skF_3') != '#skF_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_54,c_187]) ).
tff(c_196,plain,
'#skF_4'('#skF_1') = '#skF_1',
inference(demodulation,[status(thm),theory(equality)],[c_57,c_193]) ).
tff(c_198,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_80,c_196]) ).
tff(c_200,plain,
! [X_20] :
( ( g(f('#skF_2'(X_20))) = '#skF_2'(X_20) )
| ( g(f(X_20)) != X_20 ) ),
inference(splitRight,[status(thm)],[c_16]) ).
tff(c_225,plain,
! [X_21] :
( ( '#skF_2'(X_21) = '#skF_3' )
| ( g(f(X_21)) != X_21 ) ),
inference(superposition,[status(thm),theory(equality)],[c_200,c_46]) ).
tff(c_231,plain,
( ( '#skF_2'('#skF_3') = '#skF_3' )
| ( g('#skF_1') != '#skF_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_57,c_225]) ).
tff(c_234,plain,
'#skF_2'('#skF_3') = '#skF_3',
inference(demodulation,[status(thm),theory(equality)],[c_54,c_231]) ).
tff(c_236,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_160,c_234]) ).
tff(c_238,plain,
! [X_22] :
( ( f(g('#skF_4'(X_22))) = '#skF_4'(X_22) )
| ( f(g(X_22)) != X_22 ) ),
inference(splitRight,[status(thm)],[c_14]) ).
tff(c_259,plain,
! [X_23] :
( ( '#skF_4'(X_23) = '#skF_1' )
| ( f(g(X_23)) != X_23 ) ),
inference(superposition,[status(thm),theory(equality)],[c_238,c_146]) ).
tff(c_265,plain,
( ( '#skF_4'('#skF_1') = '#skF_1' )
| ( f('#skF_3') != '#skF_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_54,c_259]) ).
tff(c_268,plain,
'#skF_4'('#skF_1') = '#skF_1',
inference(demodulation,[status(thm),theory(equality)],[c_57,c_265]) ).
tff(c_270,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_80,c_268]) ).
tff(c_271,plain,
! [Y_2] :
( ( Y_2 = '#skF_1' )
| ( f(g(Y_2)) != Y_2 ) ),
inference(splitRight,[status(thm)],[c_2]) ).
tff(c_321,plain,
! [X_28] :
( ( '#skF_4'(X_28) = '#skF_1' )
| ( f(g(X_28)) != X_28 ) ),
inference(superposition,[status(thm),theory(equality)],[c_296,c_271]) ).
tff(c_327,plain,
( ( '#skF_4'('#skF_1') = '#skF_1' )
| ( f('#skF_3') != '#skF_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_54,c_321]) ).
tff(c_330,plain,
'#skF_4'('#skF_1') = '#skF_1',
inference(demodulation,[status(thm),theory(equality)],[c_57,c_327]) ).
tff(c_332,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_287,c_330]) ).
tff(c_334,plain,
! [X_29] :
( ( g(f('#skF_2'(X_29))) = '#skF_2'(X_29) )
| ( g(f(X_29)) != X_29 ) ),
inference(splitRight,[status(thm)],[c_16]) ).
tff(c_359,plain,
! [X_30] :
( ( '#skF_2'(X_30) = '#skF_3' )
| ( g(f(X_30)) != X_30 ) ),
inference(superposition,[status(thm),theory(equality)],[c_334,c_46]) ).
tff(c_365,plain,
( ( '#skF_2'('#skF_3') = '#skF_3' )
| ( g('#skF_1') != '#skF_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_57,c_359]) ).
tff(c_368,plain,
'#skF_2'('#skF_3') = '#skF_3',
inference(demodulation,[status(thm),theory(equality)],[c_54,c_365]) ).
tff(c_370,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_294,c_368]) ).
tff(c_372,plain,
! [X_31] :
( ( f(g('#skF_4'(X_31))) = '#skF_4'(X_31) )
| ( f(g(X_31)) != X_31 ) ),
inference(splitRight,[status(thm)],[c_14]) ).
tff(c_393,plain,
! [X_32] :
( ( '#skF_4'(X_32) = '#skF_1' )
| ( f(g(X_32)) != X_32 ) ),
inference(superposition,[status(thm),theory(equality)],[c_372,c_271]) ).
tff(c_399,plain,
( ( '#skF_4'('#skF_1') = '#skF_1' )
| ( f('#skF_3') != '#skF_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_54,c_393]) ).
tff(c_402,plain,
'#skF_4'('#skF_1') = '#skF_1',
inference(demodulation,[status(thm),theory(equality)],[c_57,c_399]) ).
tff(c_404,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_287,c_402]) ).
tff(c_406,plain,
! [X_33] :
( ( '#skF_2'(X_33) != X_33 )
| ( g(f(X_33)) != X_33 ) ),
inference(splitRight,[status(thm)],[c_6]) ).
tff(c_409,plain,
( ( '#skF_2'('#skF_3') != '#skF_3' )
| ( g('#skF_1') != '#skF_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_57,c_406]) ).
tff(c_411,plain,
'#skF_2'('#skF_3') != '#skF_3',
inference(demodulation,[status(thm),theory(equality)],[c_54,c_409]) ).
tff(c_8,plain,
! [X_3,X_7] :
( ( g(f('#skF_2'(X_3))) = '#skF_2'(X_3) )
| ( g(f(X_3)) != X_3 )
| ( '#skF_4'(X_7) != X_7 )
| ( f(g(X_7)) != X_7 ) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_413,plain,
! [X_34] :
( ( '#skF_4'(X_34) != X_34 )
| ( f(g(X_34)) != X_34 ) ),
inference(splitLeft,[status(thm)],[c_8]) ).
tff(c_416,plain,
( ( '#skF_4'('#skF_1') != '#skF_1' )
| ( f('#skF_3') != '#skF_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_54,c_413]) ).
tff(c_418,plain,
'#skF_4'('#skF_1') != '#skF_1',
inference(demodulation,[status(thm),theory(equality)],[c_57,c_416]) ).
tff(c_420,plain,
! [X_35] :
( ( f(g('#skF_4'(X_35))) = '#skF_4'(X_35) )
| ( f(g(X_35)) != X_35 ) ),
inference(splitLeft,[status(thm)],[c_16]) ).
tff(c_445,plain,
! [X_36] :
( ( '#skF_4'(X_36) = '#skF_1' )
| ( f(g(X_36)) != X_36 ) ),
inference(superposition,[status(thm),theory(equality)],[c_420,c_271]) ).
tff(c_451,plain,
( ( '#skF_4'('#skF_1') = '#skF_1' )
| ( f('#skF_3') != '#skF_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_54,c_445]) ).
tff(c_454,plain,
'#skF_4'('#skF_1') = '#skF_1',
inference(demodulation,[status(thm),theory(equality)],[c_57,c_451]) ).
tff(c_456,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_418,c_454]) ).
tff(c_458,plain,
! [X_37] :
( ( g(f('#skF_2'(X_37))) = '#skF_2'(X_37) )
| ( g(f(X_37)) != X_37 ) ),
inference(splitRight,[status(thm)],[c_16]) ).
tff(c_483,plain,
! [X_38] :
( ( '#skF_2'(X_38) = '#skF_3' )
| ( g(f(X_38)) != X_38 ) ),
inference(superposition,[status(thm),theory(equality)],[c_458,c_46]) ).
tff(c_489,plain,
( ( '#skF_2'('#skF_3') = '#skF_3' )
| ( g('#skF_1') != '#skF_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_57,c_483]) ).
tff(c_492,plain,
'#skF_2'('#skF_3') = '#skF_3',
inference(demodulation,[status(thm),theory(equality)],[c_54,c_489]) ).
tff(c_494,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_411,c_492]) ).
tff(c_496,plain,
! [X_39] :
( ( g(f('#skF_2'(X_39))) = '#skF_2'(X_39) )
| ( g(f(X_39)) != X_39 ) ),
inference(splitRight,[status(thm)],[c_8]) ).
tff(c_517,plain,
! [X_40] :
( ( '#skF_2'(X_40) = '#skF_3' )
| ( g(f(X_40)) != X_40 ) ),
inference(superposition,[status(thm),theory(equality)],[c_496,c_46]) ).
tff(c_523,plain,
( ( '#skF_2'('#skF_3') = '#skF_3' )
| ( g('#skF_1') != '#skF_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_57,c_517]) ).
tff(c_526,plain,
'#skF_2'('#skF_3') = '#skF_3',
inference(demodulation,[status(thm),theory(equality)],[c_54,c_523]) ).
tff(c_528,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_411,c_526]) ).
tff(c_530,plain,
! [Y_41] :
( ( Y_41 = '#skF_1' )
| ( f(g(Y_41)) != Y_41 ) ),
inference(splitRight,[status(thm)],[c_18]) ).
tff(c_539,plain,
f('#skF_3') = '#skF_1',
inference(superposition,[status(thm),theory(equality)],[c_33,c_530]) ).
tff(c_540,plain,
g('#skF_1') = '#skF_3',
inference(demodulation,[status(thm),theory(equality)],[c_539,c_33]) ).
tff(c_852,plain,
! [X_58] :
( ( '#skF_4'(X_58) != X_58 )
| ( f(g(X_58)) != X_58 ) ),
inference(splitLeft,[status(thm)],[c_6]) ).
tff(c_855,plain,
( ( '#skF_4'('#skF_1') != '#skF_1' )
| ( f('#skF_3') != '#skF_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_540,c_852]) ).
tff(c_857,plain,
'#skF_4'('#skF_1') != '#skF_1',
inference(demodulation,[status(thm),theory(equality)],[c_539,c_855]) ).
tff(c_859,plain,
! [X_59] :
( ( '#skF_2'(X_59) != X_59 )
| ( g(f(X_59)) != X_59 ) ),
inference(splitLeft,[status(thm)],[c_14]) ).
tff(c_862,plain,
( ( '#skF_2'('#skF_3') != '#skF_3' )
| ( g('#skF_1') != '#skF_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_539,c_859]) ).
tff(c_864,plain,
'#skF_2'('#skF_3') != '#skF_3',
inference(demodulation,[status(thm),theory(equality)],[c_540,c_862]) ).
tff(c_866,plain,
! [X_60] :
( ( f(g('#skF_4'(X_60))) = '#skF_4'(X_60) )
| ( f(g(X_60)) != X_60 ) ),
inference(splitLeft,[status(thm)],[c_16]) ).
tff(c_529,plain,
! [Y_2] :
( ( Y_2 = '#skF_1' )
| ( f(g(Y_2)) != Y_2 ) ),
inference(splitRight,[status(thm)],[c_18]) ).
tff(c_891,plain,
! [X_61] :
( ( '#skF_4'(X_61) = '#skF_1' )
| ( f(g(X_61)) != X_61 ) ),
inference(superposition,[status(thm),theory(equality)],[c_866,c_529]) ).
tff(c_897,plain,
( ( '#skF_4'('#skF_1') = '#skF_1' )
| ( f('#skF_3') != '#skF_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_540,c_891]) ).
tff(c_900,plain,
'#skF_4'('#skF_1') = '#skF_1',
inference(demodulation,[status(thm),theory(equality)],[c_539,c_897]) ).
tff(c_902,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_857,c_900]) ).
tff(c_904,plain,
! [X_62] :
( ( g(f('#skF_2'(X_62))) = '#skF_2'(X_62) )
| ( g(f(X_62)) != X_62 ) ),
inference(splitRight,[status(thm)],[c_16]) ).
tff(c_22,plain,
! [X_3,Y_6] :
( ( '#skF_2'(X_3) != X_3 )
| ( g(f(X_3)) != X_3 )
| ( Y_6 = '#skF_3' )
| ( g(f(Y_6)) != Y_6 ) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_558,plain,
! [X_42] :
( ( '#skF_2'(X_42) != X_42 )
| ( g(f(X_42)) != X_42 ) ),
inference(splitLeft,[status(thm)],[c_22]) ).
tff(c_561,plain,
( ( '#skF_2'('#skF_3') != '#skF_3' )
| ( g('#skF_1') != '#skF_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_539,c_558]) ).
tff(c_563,plain,
'#skF_2'('#skF_3') != '#skF_3',
inference(demodulation,[status(thm),theory(equality)],[c_540,c_561]) ).
tff(c_575,plain,
! [X_44] :
( ( '#skF_4'(X_44) != X_44 )
| ( f(g(X_44)) != X_44 ) ),
inference(splitLeft,[status(thm)],[c_8]) ).
tff(c_578,plain,
( ( '#skF_4'('#skF_1') != '#skF_1' )
| ( f('#skF_3') != '#skF_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_540,c_575]) ).
tff(c_580,plain,
'#skF_4'('#skF_1') != '#skF_1',
inference(demodulation,[status(thm),theory(equality)],[c_539,c_578]) ).
tff(c_582,plain,
! [X_45] :
( ( f(g('#skF_4'(X_45))) = '#skF_4'(X_45) )
| ( f(g(X_45)) != X_45 ) ),
inference(splitLeft,[status(thm)],[c_16]) ).
tff(c_607,plain,
! [X_46] :
( ( '#skF_4'(X_46) = '#skF_1' )
| ( f(g(X_46)) != X_46 ) ),
inference(superposition,[status(thm),theory(equality)],[c_582,c_529]) ).
tff(c_613,plain,
( ( '#skF_4'('#skF_1') = '#skF_1' )
| ( f('#skF_3') != '#skF_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_540,c_607]) ).
tff(c_616,plain,
'#skF_4'('#skF_1') = '#skF_1',
inference(demodulation,[status(thm),theory(equality)],[c_539,c_613]) ).
tff(c_618,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_580,c_616]) ).
tff(c_620,plain,
! [X_47] :
( ( g(f('#skF_2'(X_47))) = '#skF_2'(X_47) )
| ( g(f(X_47)) != X_47 ) ),
inference(splitRight,[status(thm)],[c_16]) ).
tff(c_24,plain,
! [X_3,Y_6] :
( ( g(f('#skF_2'(X_3))) = '#skF_2'(X_3) )
| ( g(f(X_3)) != X_3 )
| ( Y_6 = '#skF_3' )
| ( g(f(Y_6)) != Y_6 ) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_566,plain,
! [Y_6] :
( ( Y_6 = '#skF_3' )
| ( g(f(Y_6)) != Y_6 ) ),
inference(splitLeft,[status(thm)],[c_24]) ).
tff(c_645,plain,
! [X_48] :
( ( '#skF_2'(X_48) = '#skF_3' )
| ( g(f(X_48)) != X_48 ) ),
inference(superposition,[status(thm),theory(equality)],[c_620,c_566]) ).
tff(c_651,plain,
( ( '#skF_2'('#skF_3') = '#skF_3' )
| ( g('#skF_1') != '#skF_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_539,c_645]) ).
tff(c_654,plain,
'#skF_2'('#skF_3') = '#skF_3',
inference(demodulation,[status(thm),theory(equality)],[c_540,c_651]) ).
tff(c_656,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_563,c_654]) ).
tff(c_739,plain,
! [X_53] :
( ( g(f('#skF_2'(X_53))) = '#skF_2'(X_53) )
| ( g(f(X_53)) != X_53 ) ),
inference(splitRight,[status(thm)],[c_8]) ).
tff(c_768,plain,
! [X_54] :
( ( '#skF_2'(X_54) = '#skF_3' )
| ( g(f(X_54)) != X_54 ) ),
inference(superposition,[status(thm),theory(equality)],[c_739,c_566]) ).
tff(c_777,plain,
( ( '#skF_2'('#skF_3') = '#skF_3' )
| ( g('#skF_1') != '#skF_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_539,c_768]) ).
tff(c_781,plain,
'#skF_2'('#skF_3') = '#skF_3',
inference(demodulation,[status(thm),theory(equality)],[c_540,c_777]) ).
tff(c_783,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_563,c_781]) ).
tff(c_785,plain,
! [X_55] :
( ( g(f('#skF_2'(X_55))) = '#skF_2'(X_55) )
| ( g(f(X_55)) != X_55 ) ),
inference(splitRight,[status(thm)],[c_24]) ).
tff(c_802,plain,
! [X_56] :
( ( f('#skF_2'(X_56)) = '#skF_1' )
| ( g(f(X_56)) != X_56 ) ),
inference(superposition,[status(thm),theory(equality)],[c_785,c_529]) ).
tff(c_808,plain,
( ( f('#skF_2'('#skF_3')) = '#skF_1' )
| ( g('#skF_1') != '#skF_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_539,c_802]) ).
tff(c_811,plain,
f('#skF_2'('#skF_3')) = '#skF_1',
inference(demodulation,[status(thm),theory(equality)],[c_540,c_808]) ).
tff(c_784,plain,
! [X_3] :
( ( g(f('#skF_2'(X_3))) = '#skF_2'(X_3) )
| ( g(f(X_3)) != X_3 ) ),
inference(splitRight,[status(thm)],[c_24]) ).
tff(c_818,plain,
( ( g('#skF_1') = '#skF_2'('#skF_3') )
| ( g(f('#skF_3')) != '#skF_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_811,c_784]) ).
tff(c_826,plain,
'#skF_2'('#skF_3') = '#skF_3',
inference(demodulation,[status(thm),theory(equality)],[c_540,c_539,c_540,c_818]) ).
tff(c_828,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_563,c_826]) ).
tff(c_829,plain,
! [Y_6] :
( ( Y_6 = '#skF_3' )
| ( g(f(Y_6)) != Y_6 ) ),
inference(splitRight,[status(thm)],[c_22]) ).
tff(c_929,plain,
! [X_63] :
( ( '#skF_2'(X_63) = '#skF_3' )
| ( g(f(X_63)) != X_63 ) ),
inference(superposition,[status(thm),theory(equality)],[c_904,c_829]) ).
tff(c_935,plain,
( ( '#skF_2'('#skF_3') = '#skF_3' )
| ( g('#skF_1') != '#skF_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_539,c_929]) ).
tff(c_938,plain,
'#skF_2'('#skF_3') = '#skF_3',
inference(demodulation,[status(thm),theory(equality)],[c_540,c_935]) ).
tff(c_940,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_864,c_938]) ).
tff(c_942,plain,
! [X_64] :
( ( f(g('#skF_4'(X_64))) = '#skF_4'(X_64) )
| ( f(g(X_64)) != X_64 ) ),
inference(splitRight,[status(thm)],[c_14]) ).
tff(c_963,plain,
! [X_65] :
( ( '#skF_4'(X_65) = '#skF_1' )
| ( f(g(X_65)) != X_65 ) ),
inference(superposition,[status(thm),theory(equality)],[c_942,c_529]) ).
tff(c_969,plain,
( ( '#skF_4'('#skF_1') = '#skF_1' )
| ( f('#skF_3') != '#skF_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_540,c_963]) ).
tff(c_972,plain,
'#skF_4'('#skF_1') = '#skF_1',
inference(demodulation,[status(thm),theory(equality)],[c_539,c_969]) ).
tff(c_974,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_857,c_972]) ).
tff(c_976,plain,
! [X_66] :
( ( '#skF_2'(X_66) != X_66 )
| ( g(f(X_66)) != X_66 ) ),
inference(splitRight,[status(thm)],[c_6]) ).
tff(c_979,plain,
( ( '#skF_2'('#skF_3') != '#skF_3' )
| ( g('#skF_1') != '#skF_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_539,c_976]) ).
tff(c_981,plain,
'#skF_2'('#skF_3') != '#skF_3',
inference(demodulation,[status(thm),theory(equality)],[c_540,c_979]) ).
tff(c_983,plain,
! [X_67] :
( ( '#skF_4'(X_67) != X_67 )
| ( f(g(X_67)) != X_67 ) ),
inference(splitLeft,[status(thm)],[c_8]) ).
tff(c_986,plain,
( ( '#skF_4'('#skF_1') != '#skF_1' )
| ( f('#skF_3') != '#skF_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_540,c_983]) ).
tff(c_988,plain,
'#skF_4'('#skF_1') != '#skF_1',
inference(demodulation,[status(thm),theory(equality)],[c_539,c_986]) ).
tff(c_990,plain,
! [X_68] :
( ( f(g('#skF_4'(X_68))) = '#skF_4'(X_68) )
| ( f(g(X_68)) != X_68 ) ),
inference(splitLeft,[status(thm)],[c_16]) ).
tff(c_1015,plain,
! [X_69] :
( ( '#skF_4'(X_69) = '#skF_1' )
| ( f(g(X_69)) != X_69 ) ),
inference(superposition,[status(thm),theory(equality)],[c_990,c_529]) ).
tff(c_1021,plain,
( ( '#skF_4'('#skF_1') = '#skF_1' )
| ( f('#skF_3') != '#skF_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_540,c_1015]) ).
tff(c_1024,plain,
'#skF_4'('#skF_1') = '#skF_1',
inference(demodulation,[status(thm),theory(equality)],[c_539,c_1021]) ).
tff(c_1026,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_988,c_1024]) ).
tff(c_1028,plain,
! [X_70] :
( ( g(f('#skF_2'(X_70))) = '#skF_2'(X_70) )
| ( g(f(X_70)) != X_70 ) ),
inference(splitRight,[status(thm)],[c_16]) ).
tff(c_1053,plain,
! [X_71] :
( ( '#skF_2'(X_71) = '#skF_3' )
| ( g(f(X_71)) != X_71 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1028,c_829]) ).
tff(c_1059,plain,
( ( '#skF_2'('#skF_3') = '#skF_3' )
| ( g('#skF_1') != '#skF_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_539,c_1053]) ).
tff(c_1062,plain,
'#skF_2'('#skF_3') = '#skF_3',
inference(demodulation,[status(thm),theory(equality)],[c_540,c_1059]) ).
tff(c_1064,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_981,c_1062]) ).
tff(c_1066,plain,
! [X_72] :
( ( g(f('#skF_2'(X_72))) = '#skF_2'(X_72) )
| ( g(f(X_72)) != X_72 ) ),
inference(splitRight,[status(thm)],[c_8]) ).
tff(c_1087,plain,
! [X_73] :
( ( '#skF_2'(X_73) = '#skF_3' )
| ( g(f(X_73)) != X_73 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1066,c_829]) ).
tff(c_1093,plain,
( ( '#skF_2'('#skF_3') = '#skF_3' )
| ( g('#skF_1') != '#skF_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_539,c_1087]) ).
tff(c_1096,plain,
'#skF_2'('#skF_3') = '#skF_3',
inference(demodulation,[status(thm),theory(equality)],[c_540,c_1093]) ).
tff(c_1098,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_981,c_1096]) ).
tff(c_1100,plain,
f(g('#skF_1')) != '#skF_1',
inference(splitRight,[status(thm)],[c_20]) ).
tff(c_4,plain,
! [X_7] :
( ( f(g('#skF_1')) = '#skF_1' )
| ( '#skF_4'(X_7) != X_7 )
| ( f(g(X_7)) != X_7 ) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_1109,plain,
! [X_75] :
( ( '#skF_4'(X_75) != X_75 )
| ( f(g(X_75)) != X_75 ) ),
inference(negUnitSimplification,[status(thm)],[c_1100,c_4]) ).
tff(c_1113,plain,
'#skF_4'(f('#skF_3')) != f('#skF_3'),
inference(superposition,[status(thm),theory(equality)],[c_33,c_1109]) ).
tff(c_12,plain,
! [X_7] :
( ( f(g('#skF_1')) = '#skF_1' )
| ( f(g('#skF_4'(X_7))) = '#skF_4'(X_7) )
| ( f(g(X_7)) != X_7 ) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_1116,plain,
! [X_76] :
( ( f(g('#skF_4'(X_76))) = '#skF_4'(X_76) )
| ( f(g(X_76)) != X_76 ) ),
inference(negUnitSimplification,[status(thm)],[c_1100,c_12]) ).
tff(c_1099,plain,
! [Y_6] :
( ( Y_6 = '#skF_3' )
| ( g(f(Y_6)) != Y_6 ) ),
inference(splitRight,[status(thm)],[c_20]) ).
tff(c_1133,plain,
! [X_77] :
( ( g('#skF_4'(X_77)) = '#skF_3' )
| ( f(g(X_77)) != X_77 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1116,c_1099]) ).
tff(c_1115,plain,
! [X_7] :
( ( f(g('#skF_4'(X_7))) = '#skF_4'(X_7) )
| ( f(g(X_7)) != X_7 ) ),
inference(negUnitSimplification,[status(thm)],[c_1100,c_12]) ).
tff(c_1161,plain,
! [X_80] :
( ( f('#skF_3') = '#skF_4'(X_80) )
| ( f(g(X_80)) != X_80 )
| ( f(g(X_80)) != X_80 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1133,c_1115]) ).
tff(c_1167,plain,
( ( '#skF_4'(f('#skF_3')) = f('#skF_3') )
| ( f(g(f('#skF_3'))) != f('#skF_3') ) ),
inference(superposition,[status(thm),theory(equality)],[c_33,c_1161]) ).
tff(c_1171,plain,
'#skF_4'(f('#skF_3')) = f('#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_33,c_1167]) ).
tff(c_1173,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1113,c_1171]) ).
tff(c_1174,plain,
f(g('#skF_1')) = '#skF_1',
inference(splitRight,[status(thm)],[c_28]) ).
tff(c_1175,plain,
g(f('#skF_3')) != '#skF_3',
inference(splitRight,[status(thm)],[c_28]) ).
tff(c_30,plain,
! [X_3] :
( ( '#skF_2'(X_3) != X_3 )
| ( g(f(X_3)) != X_3 )
| ( g(f('#skF_3')) = '#skF_3' ) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_1189,plain,
! [X_82] :
( ( '#skF_2'(X_82) != X_82 )
| ( g(f(X_82)) != X_82 ) ),
inference(negUnitSimplification,[status(thm)],[c_1175,c_30]) ).
tff(c_1193,plain,
'#skF_2'(g('#skF_1')) != g('#skF_1'),
inference(superposition,[status(thm),theory(equality)],[c_1174,c_1189]) ).
tff(c_32,plain,
! [X_3] :
( ( g(f('#skF_2'(X_3))) = '#skF_2'(X_3) )
| ( g(f(X_3)) != X_3 )
| ( g(f('#skF_3')) = '#skF_3' ) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_1196,plain,
! [X_83] :
( ( g(f('#skF_2'(X_83))) = '#skF_2'(X_83) )
| ( g(f(X_83)) != X_83 ) ),
inference(negUnitSimplification,[status(thm)],[c_1175,c_32]) ).
tff(c_26,plain,
! [Y_2] :
( ( Y_2 = '#skF_1' )
| ( f(g(Y_2)) != Y_2 )
| ( g(f('#skF_3')) = '#skF_3' ) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_1180,plain,
! [Y_2] :
( ( Y_2 = '#skF_1' )
| ( f(g(Y_2)) != Y_2 ) ),
inference(negUnitSimplification,[status(thm)],[c_1175,c_26]) ).
tff(c_1213,plain,
! [X_84] :
( ( f('#skF_2'(X_84)) = '#skF_1' )
| ( g(f(X_84)) != X_84 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1196,c_1180]) ).
tff(c_1221,plain,
f('#skF_2'(g('#skF_1'))) = '#skF_1',
inference(superposition,[status(thm),theory(equality)],[c_1174,c_1213]) ).
tff(c_1195,plain,
! [X_3] :
( ( g(f('#skF_2'(X_3))) = '#skF_2'(X_3) )
| ( g(f(X_3)) != X_3 ) ),
inference(negUnitSimplification,[status(thm)],[c_1175,c_32]) ).
tff(c_1229,plain,
( ( '#skF_2'(g('#skF_1')) = g('#skF_1') )
| ( g(f(g('#skF_1'))) != g('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_1221,c_1195]) ).
tff(c_1236,plain,
'#skF_2'(g('#skF_1')) = g('#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_1174,c_1229]) ).
tff(c_1238,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1193,c_1236]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN417+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 17:56:37 EDT 2023
% 0.13/0.35 % CPUTime :
% 3.87/2.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.00/2.05
% 4.00/2.05 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.00/2.12
% 4.00/2.12 Inference rules
% 4.00/2.12 ----------------------
% 4.00/2.12 #Ref : 0
% 4.00/2.12 #Sup : 253
% 4.00/2.12 #Fact : 0
% 4.00/2.12 #Define : 0
% 4.00/2.12 #Split : 22
% 4.00/2.12 #Chain : 0
% 4.00/2.12 #Close : 0
% 4.00/2.12
% 4.00/2.12 Ordering : KBO
% 4.00/2.12
% 4.00/2.12 Simplification rules
% 4.00/2.12 ----------------------
% 4.00/2.12 #Subsume : 38
% 4.00/2.12 #Demod : 100
% 4.00/2.12 #Tautology : 105
% 4.00/2.12 #SimpNegUnit : 27
% 4.00/2.12 #BackRed : 5
% 4.00/2.12
% 4.00/2.12 #Partial instantiations: 0
% 4.00/2.12 #Strategies tried : 1
% 4.00/2.12
% 4.00/2.12 Timing (in seconds)
% 4.00/2.12 ----------------------
% 4.00/2.12 Preprocessing : 0.44
% 4.00/2.12 Parsing : 0.23
% 4.00/2.12 CNF conversion : 0.03
% 4.00/2.12 Main loop : 0.55
% 4.00/2.12 Inferencing : 0.22
% 4.00/2.12 Reduction : 0.12
% 4.00/2.12 Demodulation : 0.08
% 4.00/2.12 BG Simplification : 0.03
% 4.00/2.13 Subsumption : 0.12
% 4.00/2.13 Abstraction : 0.04
% 4.00/2.13 MUC search : 0.00
% 4.00/2.13 Cooper : 0.00
% 4.00/2.13 Total : 1.10
% 4.00/2.13 Index Insertion : 0.00
% 4.00/2.13 Index Deletion : 0.00
% 4.00/2.13 Index Matching : 0.00
% 4.00/2.13 BG Taut test : 0.00
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