TSTP Solution File: GRP776+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRP776+1 : TPTP v8.1.2. Released v4.1.0.
% 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 : n025.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 10:42:06 EDT 2023
% Result : Theorem 31.02s 14.17s
% Output : CNFRefutation 31.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 29
% Syntax : Number of formulae : 140 ( 53 unt; 10 typ; 0 def)
% Number of atoms : 256 ( 89 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 244 ( 118 ~; 104 |; 7 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 7 >; 2 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 104 (; 104 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ h > g > sum > product > #nlpp > opp > inv > f > eh > eg > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(h,type,
h: $i > $o ).
tff(opp,type,
opp: $i > $i ).
tff(f,type,
f: $i > $i ).
tff(inv,type,
inv: $i > $i ).
tff(product,type,
product: ( $i * $i ) > $i ).
tff(eh,type,
eh: $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(sum,type,
sum: ( $i * $i ) > $i ).
tff(eg,type,
eg: $i ).
tff(g,type,
g: $i > $o ).
tff(f_115,negated_conjecture,
~ ! [X0] :
( ( f(eh) = eg )
& ( ~ g(X0)
| ( f(inv(X0)) = opp(f(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
tff(f_37,axiom,
g(eh),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).
tff(f_104,axiom,
! [A] :
( g(A)
=> h(f(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos17) ).
tff(f_36,axiom,
! [A] :
( g(A)
=> g(inv(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos02) ).
tff(f_50,axiom,
! [A] :
( g(A)
=> ( product(eh,A) = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).
tff(f_58,axiom,
! [A] :
( g(A)
=> ( product(A,inv(A)) = eh ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos07) ).
tff(f_62,axiom,
! [A] :
( g(A)
=> ( product(inv(A),A) = eh ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos08) ).
tff(f_106,axiom,
! [B,A] : ( f(product(A,B)) = sum(f(A),f(B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos18) ).
tff(f_69,axiom,
! [B,A] :
( ( h(A)
& h(B) )
=> h(sum(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos09) ).
tff(f_74,axiom,
h(eg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos11) ).
tff(f_87,axiom,
! [A] :
( h(A)
=> ( sum(eg,A) = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos13) ).
tff(f_91,axiom,
! [A] :
( h(A)
=> ( sum(A,eg) = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos14) ).
tff(f_73,axiom,
! [B,A] :
( h(A)
=> h(opp(B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos10) ).
tff(f_99,axiom,
! [A] :
( h(A)
=> ( sum(opp(A),A) = eg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos16) ).
tff(f_83,axiom,
! [C,B,A] :
( ( h(A)
& h(B)
& h(C) )
=> ( sum(sum(A,B),C) = sum(A,sum(B,C)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos12) ).
tff(f_54,axiom,
! [A] :
( g(A)
=> ( product(A,eh) = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).
tff(f_32,axiom,
! [B,A] :
( ( g(A)
& g(B) )
=> g(product(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos01) ).
tff(f_46,axiom,
! [C,B,A] :
( ( g(A)
& g(B)
& g(C) )
=> ( product(product(A,B),C) = product(A,product(B,C)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).
tff(f_95,axiom,
! [A] :
( h(A)
=> ( sum(A,opp(A)) = eg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos15) ).
tff(c_40,plain,
( g('#skF_1')
| ( f(eh) != eg ) ),
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_41,plain,
f(eh) != eg,
inference(splitLeft,[status(thm)],[c_40]) ).
tff(c_6,plain,
g(eh),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_34,plain,
! [A_22] :
( h(f(A_22))
| ~ g(A_22) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_4,plain,
! [A_3] :
( g(inv(A_3))
| ~ g(A_3) ),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_94,plain,
! [A_31] :
( ( product(eh,A_31) = A_31 )
| ~ g(A_31) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_264,plain,
! [A_42] :
( ( product(eh,inv(A_42)) = inv(A_42) )
| ~ g(A_42) ),
inference(resolution,[status(thm)],[c_4,c_94]) ).
tff(c_14,plain,
! [A_9] :
( ( product(A_9,inv(A_9)) = eh )
| ~ g(A_9) ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_274,plain,
( ( inv(eh) = eh )
| ~ g(eh)
| ~ g(eh) ),
inference(superposition,[status(thm),theory(equality)],[c_264,c_14]) ).
tff(c_286,plain,
inv(eh) = eh,
inference(demodulation,[status(thm),theory(equality)],[c_6,c_6,c_274]) ).
tff(c_16,plain,
! [A_10] :
( ( product(inv(A_10),A_10) = eh )
| ~ g(A_10) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_315,plain,
! [A_43,B_44] : ( sum(f(A_43),f(B_44)) = f(product(A_43,B_44)) ),
inference(cnfTransformation,[status(thm)],[f_106]) ).
tff(c_18,plain,
! [A_12,B_11] :
( h(sum(A_12,B_11))
| ~ h(B_11)
| ~ h(A_12) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_386,plain,
! [A_48,B_49] :
( h(f(product(A_48,B_49)))
| ~ h(f(B_49))
| ~ h(f(A_48)) ),
inference(superposition,[status(thm),theory(equality)],[c_315,c_18]) ).
tff(c_401,plain,
! [A_10] :
( h(f(eh))
| ~ h(f(A_10))
| ~ h(f(inv(A_10)))
| ~ g(A_10) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_386]) ).
tff(c_989,plain,
! [A_66] :
( ~ h(f(A_66))
| ~ h(f(inv(A_66)))
| ~ g(A_66) ),
inference(splitLeft,[status(thm)],[c_401]) ).
tff(c_992,plain,
( ~ h(f(eh))
| ~ h(f(eh))
| ~ g(eh) ),
inference(superposition,[status(thm),theory(equality)],[c_286,c_989]) ).
tff(c_997,plain,
~ h(f(eh)),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_992]) ).
tff(c_1001,plain,
~ g(eh),
inference(resolution,[status(thm)],[c_34,c_997]) ).
tff(c_1005,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6,c_1001]) ).
tff(c_1006,plain,
h(f(eh)),
inference(splitRight,[status(thm)],[c_401]) ).
tff(c_22,plain,
h(eg),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_50,plain,
! [A_28] :
( ( sum(eg,A_28) = A_28 )
| ~ h(A_28) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_62,plain,
sum(eg,eg) = eg,
inference(resolution,[status(thm)],[c_22,c_50]) ).
tff(c_28,plain,
! [A_19] :
( ( sum(A_19,eg) = A_19 )
| ~ h(A_19) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_1091,plain,
sum(f(eh),eg) = f(eh),
inference(resolution,[status(thm)],[c_1006,c_28]) ).
tff(c_20,plain,
! [B_13,A_14] :
( h(opp(B_13))
| ~ h(A_14) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_44,plain,
! [A_14] : ~ h(A_14),
inference(splitLeft,[status(thm)],[c_20]) ).
tff(c_47,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_44,c_22]) ).
tff(c_48,plain,
! [B_13] : h(opp(B_13)),
inference(splitRight,[status(thm)],[c_20]) ).
tff(c_32,plain,
! [A_21] :
( ( sum(opp(A_21),A_21) = eg )
| ~ h(A_21) ),
inference(cnfTransformation,[status(thm)],[f_99]) ).
tff(c_742,plain,
! [A_60,B_61,C_62] :
( ( sum(sum(A_60,B_61),C_62) = sum(A_60,sum(B_61,C_62)) )
| ~ h(C_62)
| ~ h(B_61)
| ~ h(A_60) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_779,plain,
! [A_21,C_62] :
( ( sum(opp(A_21),sum(A_21,C_62)) = sum(eg,C_62) )
| ~ h(C_62)
| ~ h(A_21)
| ~ h(opp(A_21))
| ~ h(A_21) ),
inference(superposition,[status(thm),theory(equality)],[c_32,c_742]) ).
tff(c_1330,plain,
! [A_72,C_73] :
( ( sum(opp(A_72),sum(A_72,C_73)) = sum(eg,C_73) )
| ~ h(C_73)
| ~ h(A_72) ),
inference(demodulation,[status(thm),theory(equality)],[c_48,c_779]) ).
tff(c_1369,plain,
( ( sum(opp(f(eh)),f(eh)) = sum(eg,eg) )
| ~ h(eg)
| ~ h(f(eh)) ),
inference(superposition,[status(thm),theory(equality)],[c_1091,c_1330]) ).
tff(c_1431,plain,
sum(opp(f(eh)),f(eh)) = eg,
inference(demodulation,[status(thm),theory(equality)],[c_1006,c_22,c_62,c_1369]) ).
tff(c_26,plain,
! [A_18] :
( ( sum(eg,A_18) = A_18 )
| ~ h(A_18) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_1092,plain,
sum(eg,f(eh)) = f(eh),
inference(resolution,[status(thm)],[c_1006,c_26]) ).
tff(c_81,plain,
! [A_30] :
( ( product(A_30,eh) = A_30 )
| ~ g(A_30) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_89,plain,
product(eh,eh) = eh,
inference(resolution,[status(thm)],[c_6,c_81]) ).
tff(c_36,plain,
! [A_24,B_23] : ( sum(f(A_24),f(B_23)) = f(product(A_24,B_23)) ),
inference(cnfTransformation,[status(thm)],[f_106]) ).
tff(c_60946,plain,
! [A_292,B_293] :
( ( sum(opp(f(A_292)),f(product(A_292,B_293))) = sum(eg,f(B_293)) )
| ~ h(f(B_293))
| ~ h(f(A_292)) ),
inference(superposition,[status(thm),theory(equality)],[c_36,c_1330]) ).
tff(c_61051,plain,
( ( sum(opp(f(eh)),f(eh)) = sum(eg,f(eh)) )
| ~ h(f(eh))
| ~ h(f(eh)) ),
inference(superposition,[status(thm),theory(equality)],[c_89,c_60946]) ).
tff(c_61093,plain,
f(eh) = eg,
inference(demodulation,[status(thm),theory(equality)],[c_1006,c_1006,c_1431,c_1092,c_61051]) ).
tff(c_61095,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_41,c_61093]) ).
tff(c_61097,plain,
f(eh) = eg,
inference(splitRight,[status(thm)],[c_40]) ).
tff(c_38,plain,
( ( opp(f('#skF_1')) != f(inv('#skF_1')) )
| ( f(eh) != eg ) ),
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_61104,plain,
opp(f('#skF_1')) != f(inv('#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_61097,c_38]) ).
tff(c_61096,plain,
g('#skF_1'),
inference(splitRight,[status(thm)],[c_40]) ).
tff(c_61169,plain,
! [A_300] :
( ( product(A_300,eh) = A_300 )
| ~ g(A_300) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_61180,plain,
product('#skF_1',eh) = '#skF_1',
inference(resolution,[status(thm)],[c_61096,c_61169]) ).
tff(c_61148,plain,
! [A_299] :
( ( product(eh,A_299) = A_299 )
| ~ g(A_299) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_61159,plain,
product(eh,'#skF_1') = '#skF_1',
inference(resolution,[status(thm)],[c_61096,c_61148]) ).
tff(c_61325,plain,
! [A_309,B_310] :
( g(product(A_309,B_310))
| ~ g(B_310)
| ~ g(A_309) ),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_12,plain,
! [A_8] :
( ( product(A_8,eh) = A_8 )
| ~ g(A_8) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_61347,plain,
! [A_309,B_310] :
( ( product(product(A_309,B_310),eh) = product(A_309,B_310) )
| ~ g(B_310)
| ~ g(A_309) ),
inference(resolution,[status(thm)],[c_61325,c_12]) ).
tff(c_61402,plain,
! [A_313,B_314] : ( sum(f(A_313),f(B_314)) = f(product(A_313,B_314)) ),
inference(cnfTransformation,[status(thm)],[f_106]) ).
tff(c_61417,plain,
! [A_313] : ( sum(f(A_313),eg) = f(product(A_313,eh)) ),
inference(superposition,[status(thm),theory(equality)],[c_61097,c_61402]) ).
tff(c_61414,plain,
! [B_314] : ( sum(eg,f(B_314)) = f(product(eh,B_314)) ),
inference(superposition,[status(thm),theory(equality)],[c_61097,c_61402]) ).
tff(c_61117,plain,
! [A_297] :
( ( sum(eg,A_297) = A_297 )
| ~ h(A_297) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_61128,plain,
! [A_22] :
( ( sum(eg,f(A_22)) = f(A_22) )
| ~ g(A_22) ),
inference(resolution,[status(thm)],[c_34,c_61117]) ).
tff(c_61514,plain,
! [A_318] :
( ( f(product(eh,A_318)) = f(A_318) )
| ~ g(A_318) ),
inference(demodulation,[status(thm),theory(equality)],[c_61414,c_61128]) ).
tff(c_61523,plain,
! [A_318] :
( ( f(product(product(eh,A_318),eh)) = sum(f(A_318),eg) )
| ~ g(A_318) ),
inference(superposition,[status(thm),theory(equality)],[c_61514,c_61417]) ).
tff(c_64403,plain,
! [A_361] :
( ( f(product(product(eh,A_361),eh)) = f(product(A_361,eh)) )
| ~ g(A_361) ),
inference(demodulation,[status(thm),theory(equality)],[c_61417,c_61523]) ).
tff(c_64454,plain,
! [B_310] :
( ( f(product(eh,B_310)) = f(product(B_310,eh)) )
| ~ g(B_310)
| ~ g(B_310)
| ~ g(eh) ),
inference(superposition,[status(thm),theory(equality)],[c_61347,c_64403]) ).
tff(c_66669,plain,
! [B_384] :
( ( f(product(eh,B_384)) = f(product(B_384,eh)) )
| ~ g(B_384) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_64454]) ).
tff(c_70845,plain,
! [B_421] :
( h(f(product(eh,B_421)))
| ~ g(product(B_421,eh))
| ~ g(B_421) ),
inference(superposition,[status(thm),theory(equality)],[c_66669,c_34]) ).
tff(c_70905,plain,
( h(f('#skF_1'))
| ~ g(product('#skF_1',eh))
| ~ g('#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_61159,c_70845]) ).
tff(c_70925,plain,
h(f('#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_61096,c_61096,c_61180,c_70905]) ).
tff(c_61160,plain,
product(eh,eh) = eh,
inference(resolution,[status(thm)],[c_6,c_61148]) ).
tff(c_61698,plain,
! [A_322,B_323,C_324] :
( ( product(product(A_322,B_323),C_324) = product(A_322,product(B_323,C_324)) )
| ~ g(C_324)
| ~ g(B_323)
| ~ g(A_322) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_61750,plain,
! [C_324] :
( ( product(eh,product('#skF_1',C_324)) = product('#skF_1',C_324) )
| ~ g(C_324)
| ~ g('#skF_1')
| ~ g(eh) ),
inference(superposition,[status(thm),theory(equality)],[c_61159,c_61698]) ).
tff(c_61807,plain,
! [C_326] :
( ( product(eh,product('#skF_1',C_326)) = product('#skF_1',C_326) )
| ~ g(C_326) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_61096,c_61750]) ).
tff(c_61835,plain,
( ( product('#skF_1',inv('#skF_1')) = product(eh,eh) )
| ~ g(inv('#skF_1'))
| ~ g('#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_61807]) ).
tff(c_61848,plain,
( ( product('#skF_1',inv('#skF_1')) = eh )
| ~ g(inv('#skF_1')) ),
inference(demodulation,[status(thm),theory(equality)],[c_61096,c_61160,c_61835]) ).
tff(c_61851,plain,
~ g(inv('#skF_1')),
inference(splitLeft,[status(thm)],[c_61848]) ).
tff(c_61921,plain,
~ g('#skF_1'),
inference(resolution,[status(thm)],[c_4,c_61851]) ).
tff(c_61925,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_61096,c_61921]) ).
tff(c_61927,plain,
g(inv('#skF_1')),
inference(splitRight,[status(thm)],[c_61848]) ).
tff(c_61934,plain,
product(inv('#skF_1'),eh) = inv('#skF_1'),
inference(resolution,[status(thm)],[c_61927,c_12]) ).
tff(c_10,plain,
! [A_7] :
( ( product(eh,A_7) = A_7 )
| ~ g(A_7) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_61935,plain,
product(eh,inv('#skF_1')) = inv('#skF_1'),
inference(resolution,[status(thm)],[c_61927,c_10]) ).
tff(c_70882,plain,
( h(f(inv('#skF_1')))
| ~ g(product(inv('#skF_1'),eh))
| ~ g(inv('#skF_1')) ),
inference(superposition,[status(thm),theory(equality)],[c_61935,c_70845]) ).
tff(c_70917,plain,
h(f(inv('#skF_1'))),
inference(demodulation,[status(thm),theory(equality)],[c_61927,c_61927,c_61934,c_70882]) ).
tff(c_61111,plain,
! [A_14] : ~ h(A_14),
inference(splitLeft,[status(thm)],[c_20]) ).
tff(c_61114,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_61111,c_22]) ).
tff(c_61115,plain,
! [B_13] : h(opp(B_13)),
inference(splitRight,[status(thm)],[c_20]) ).
tff(c_61127,plain,
! [B_13] : ( sum(eg,opp(B_13)) = opp(B_13) ),
inference(resolution,[status(thm)],[c_61115,c_61117]) ).
tff(c_61926,plain,
product('#skF_1',inv('#skF_1')) = eh,
inference(splitRight,[status(thm)],[c_61848]) ).
tff(c_8,plain,
! [A_6,B_5,C_4] :
( ( product(product(A_6,B_5),C_4) = product(A_6,product(B_5,C_4)) )
| ~ g(C_4)
| ~ g(B_5)
| ~ g(A_6) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_61942,plain,
! [C_4] :
( ( product('#skF_1',product(inv('#skF_1'),C_4)) = product(eh,C_4) )
| ~ g(C_4)
| ~ g(inv('#skF_1'))
| ~ g('#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_61926,c_8]) ).
tff(c_62629,plain,
! [C_339] :
( ( product('#skF_1',product(inv('#skF_1'),C_339)) = product(eh,C_339) )
| ~ g(C_339) ),
inference(demodulation,[status(thm),theory(equality)],[c_61096,c_61927,c_61942]) ).
tff(c_62672,plain,
( ( product(eh,inv(inv('#skF_1'))) = product('#skF_1',eh) )
| ~ g(inv(inv('#skF_1')))
| ~ g(inv('#skF_1')) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_62629]) ).
tff(c_62692,plain,
( ( product(eh,inv(inv('#skF_1'))) = '#skF_1' )
| ~ g(inv(inv('#skF_1'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_61927,c_61180,c_62672]) ).
tff(c_62695,plain,
~ g(inv(inv('#skF_1'))),
inference(splitLeft,[status(thm)],[c_62692]) ).
tff(c_62794,plain,
~ g(inv('#skF_1')),
inference(resolution,[status(thm)],[c_4,c_62695]) ).
tff(c_62798,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_61927,c_62794]) ).
tff(c_62799,plain,
product(eh,inv(inv('#skF_1'))) = '#skF_1',
inference(splitRight,[status(thm)],[c_62692]) ).
tff(c_61158,plain,
! [A_3] :
( ( product(eh,inv(A_3)) = inv(A_3) )
| ~ g(A_3) ),
inference(resolution,[status(thm)],[c_4,c_61148]) ).
tff(c_62830,plain,
( ( inv(inv('#skF_1')) = '#skF_1' )
| ~ g(inv('#skF_1')) ),
inference(superposition,[status(thm),theory(equality)],[c_62799,c_61158]) ).
tff(c_62850,plain,
inv(inv('#skF_1')) = '#skF_1',
inference(demodulation,[status(thm),theory(equality)],[c_61927,c_62830]) ).
tff(c_62869,plain,
( ( product(inv('#skF_1'),'#skF_1') = eh )
| ~ g(inv('#skF_1')) ),
inference(superposition,[status(thm),theory(equality)],[c_62850,c_14]) ).
tff(c_62883,plain,
product(inv('#skF_1'),'#skF_1') = eh,
inference(demodulation,[status(thm),theory(equality)],[c_61927,c_62869]) ).
tff(c_30,plain,
! [A_20] :
( ( sum(A_20,opp(A_20)) = eg )
| ~ h(A_20) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_62042,plain,
! [A_328,B_329,C_330] :
( ( sum(sum(A_328,B_329),C_330) = sum(A_328,sum(B_329,C_330)) )
| ~ h(C_330)
| ~ h(B_329)
| ~ h(A_328) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_70707,plain,
! [A_418,B_419,C_420] :
( ( sum(f(A_418),sum(f(B_419),C_420)) = sum(f(product(A_418,B_419)),C_420) )
| ~ h(C_420)
| ~ h(f(B_419))
| ~ h(f(A_418)) ),
inference(superposition,[status(thm),theory(equality)],[c_36,c_62042]) ).
tff(c_70817,plain,
! [A_418,B_419] :
( ( sum(f(product(A_418,B_419)),opp(f(B_419))) = sum(f(A_418),eg) )
| ~ h(opp(f(B_419)))
| ~ h(f(B_419))
| ~ h(f(A_418))
| ~ h(f(B_419)) ),
inference(superposition,[status(thm),theory(equality)],[c_30,c_70707]) ).
tff(c_125346,plain,
! [A_620,B_621] :
( ( sum(f(product(A_620,B_621)),opp(f(B_621))) = f(product(A_620,eh)) )
| ~ h(f(A_620))
| ~ h(f(B_621)) ),
inference(demodulation,[status(thm),theory(equality)],[c_61115,c_61417,c_70817]) ).
tff(c_125605,plain,
( ( sum(f(eh),opp(f('#skF_1'))) = f(product(inv('#skF_1'),eh)) )
| ~ h(f(inv('#skF_1')))
| ~ h(f('#skF_1')) ),
inference(superposition,[status(thm),theory(equality)],[c_62883,c_125346]) ).
tff(c_125785,plain,
opp(f('#skF_1')) = f(inv('#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_70925,c_70917,c_61127,c_61097,c_61934,c_125605]) ).
tff(c_125787,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_61104,c_125785]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : GRP776+1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.15 % 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
% 0.14/0.36 % Computer : n025.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Thu Aug 3 22:08:34 EDT 2023
% 0.14/0.37 % CPUTime :
% 31.02/14.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 31.02/14.19
% 31.02/14.19 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 31.21/14.25
% 31.21/14.25 Inference rules
% 31.21/14.25 ----------------------
% 31.21/14.25 #Ref : 0
% 31.21/14.25 #Sup : 28988
% 31.21/14.25 #Fact : 0
% 31.21/14.25 #Define : 0
% 31.21/14.25 #Split : 6
% 31.21/14.25 #Chain : 0
% 31.21/14.25 #Close : 0
% 31.21/14.25
% 31.21/14.25 Ordering : KBO
% 31.21/14.25
% 31.21/14.25 Simplification rules
% 31.21/14.25 ----------------------
% 31.21/14.25 #Subsume : 8121
% 31.21/14.25 #Demod : 50970
% 31.21/14.25 #Tautology : 8705
% 31.21/14.25 #SimpNegUnit : 6
% 31.21/14.25 #BackRed : 7
% 31.21/14.25
% 31.21/14.25 #Partial instantiations: 0
% 31.21/14.25 #Strategies tried : 1
% 31.21/14.25
% 31.21/14.25 Timing (in seconds)
% 31.21/14.25 ----------------------
% 31.21/14.26 Preprocessing : 0.67
% 31.21/14.26 Parsing : 0.33
% 31.21/14.26 CNF conversion : 0.05
% 31.21/14.26 Main loop : 12.32
% 31.21/14.26 Inferencing : 2.50
% 31.21/14.26 Reduction : 4.83
% 31.21/14.26 Demodulation : 4.05
% 31.21/14.26 BG Simplification : 0.22
% 31.21/14.26 Subsumption : 4.15
% 31.21/14.26 Abstraction : 0.35
% 31.21/14.26 MUC search : 0.00
% 31.21/14.26 Cooper : 0.00
% 31.21/14.26 Total : 13.09
% 31.21/14.26 Index Insertion : 0.00
% 31.21/14.26 Index Deletion : 0.00
% 31.21/14.26 Index Matching : 0.00
% 31.21/14.26 BG Taut test : 0.00
%------------------------------------------------------------------------------