%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ALG042+1 : TPTP v9.0.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Apr 9 05:24:03 PM UTC 2025
% Result : Theorem 5.82s 2.28s
% Output : CNFRefutation 6.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 85 ( 72 unt; 0 typ; 0 def)
% Number of atoms : 212 ( 202 equ)
% Maximal formula atoms : 72 ( 2 avg)
% Number of connectives : 140 ( 13 ~; 45 |; 81 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 43 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ op2 > op1 > #nlpp > j > h > e23 > e22 > e21 > e20 > e13 > e12 > e11 > e10
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(e21,type,
e21: $i ).
tff(e20,type,
e20: $i ).
tff(e13,type,
e13: $i ).
tff(e22,type,
e22: $i ).
tff(op2,type,
op2: ( $i * $i ) > $i ).
tff(op1,type,
op1: ( $i * $i ) > $i ).
tff(e10,type,
e10: $i ).
tff(h,type,
h: $i > $i ).
tff(e23,type,
e23: $i ).
tff(e12,type,
e12: $i ).
tff(j,type,
j: $i > $i ).
tff(e11,type,
e11: $i ).
tff(f_59,axiom,
( ( e20 != e21 )
& ( e20 != e22 )
& ( e20 != e23 )
& ( e21 != e22 )
& ( e21 != e23 )
& ( e22 != e23 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
tff(f_168,axiom,
( ( op2(e20,e20) = e20 )
& ( op2(e20,e21) = e21 )
& ( op2(e20,e22) = e22 )
& ( op2(e20,e23) = e23 )
& ( op2(e21,e20) = e21 )
& ( op2(e21,e21) = e23 )
& ( op2(e21,e22) = e20 )
& ( op2(e21,e23) = e22 )
& ( op2(e22,e20) = e22 )
& ( op2(e22,e21) = e20 )
& ( op2(e22,e22) = e23 )
& ( op2(e22,e23) = e21 )
& ( op2(e23,e20) = e23 )
& ( op2(e23,e21) = e22 )
& ( op2(e23,e22) = e21 )
& ( op2(e23,e23) = e20 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
tff(f_313,negated_conjecture,
~ ( ( ( ( h(e10) = e20 )
| ( h(e10) = e21 )
| ( h(e10) = e22 )
| ( h(e10) = e23 ) )
& ( ( h(e11) = e20 )
| ( h(e11) = e21 )
| ( h(e11) = e22 )
| ( h(e11) = e23 ) )
& ( ( h(e12) = e20 )
| ( h(e12) = e21 )
| ( h(e12) = e22 )
| ( h(e12) = e23 ) )
& ( ( h(e13) = e20 )
| ( h(e13) = e21 )
| ( h(e13) = e22 )
| ( h(e13) = e23 ) )
& ( ( j(e20) = e10 )
| ( j(e20) = e11 )
| ( j(e20) = e12 )
| ( j(e20) = e13 ) )
& ( ( j(e21) = e10 )
| ( j(e21) = e11 )
| ( j(e21) = e12 )
| ( j(e21) = e13 ) )
& ( ( j(e22) = e10 )
| ( j(e22) = e11 )
| ( j(e22) = e12 )
| ( j(e22) = e13 ) )
& ( ( j(e23) = e10 )
| ( j(e23) = e11 )
| ( j(e23) = e12 )
| ( j(e23) = e13 ) ) )
=> ~ ( ( h(op1(e10,e10)) = op2(h(e10),h(e10)) )
& ( h(op1(e10,e11)) = op2(h(e10),h(e11)) )
& ( h(op1(e10,e12)) = op2(h(e10),h(e12)) )
& ( h(op1(e10,e13)) = op2(h(e10),h(e13)) )
& ( h(op1(e11,e10)) = op2(h(e11),h(e10)) )
& ( h(op1(e11,e11)) = op2(h(e11),h(e11)) )
& ( h(op1(e11,e12)) = op2(h(e11),h(e12)) )
& ( h(op1(e11,e13)) = op2(h(e11),h(e13)) )
& ( h(op1(e12,e10)) = op2(h(e12),h(e10)) )
& ( h(op1(e12,e11)) = op2(h(e12),h(e11)) )
& ( h(op1(e12,e12)) = op2(h(e12),h(e12)) )
& ( h(op1(e12,e13)) = op2(h(e12),h(e13)) )
& ( h(op1(e13,e10)) = op2(h(e13),h(e10)) )
& ( h(op1(e13,e11)) = op2(h(e13),h(e11)) )
& ( h(op1(e13,e12)) = op2(h(e13),h(e12)) )
& ( h(op1(e13,e13)) = op2(h(e13),h(e13)) )
& ( j(op2(e20,e20)) = op1(j(e20),j(e20)) )
& ( j(op2(e20,e21)) = op1(j(e20),j(e21)) )
& ( j(op2(e20,e22)) = op1(j(e20),j(e22)) )
& ( j(op2(e20,e23)) = op1(j(e20),j(e23)) )
& ( j(op2(e21,e20)) = op1(j(e21),j(e20)) )
& ( j(op2(e21,e21)) = op1(j(e21),j(e21)) )
& ( j(op2(e21,e22)) = op1(j(e21),j(e22)) )
& ( j(op2(e21,e23)) = op1(j(e21),j(e23)) )
& ( j(op2(e22,e20)) = op1(j(e22),j(e20)) )
& ( j(op2(e22,e21)) = op1(j(e22),j(e21)) )
& ( j(op2(e22,e22)) = op1(j(e22),j(e22)) )
& ( j(op2(e22,e23)) = op1(j(e22),j(e23)) )
& ( j(op2(e23,e20)) = op1(j(e23),j(e20)) )
& ( j(op2(e23,e21)) = op1(j(e23),j(e21)) )
& ( j(op2(e23,e22)) = op1(j(e23),j(e22)) )
& ( j(op2(e23,e23)) = op1(j(e23),j(e23)) )
& ( h(j(e20)) = e20 )
& ( h(j(e21)) = e21 )
& ( h(j(e22)) = e22 )
& ( h(j(e23)) = e23 )
& ( j(h(e10)) = e10 )
& ( j(h(e11)) = e11 )
& ( j(h(e12)) = e12 )
& ( j(h(e13)) = e13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f_137,axiom,
( ( op1(e10,e10) = e10 )
& ( op1(e10,e11) = e11 )
& ( op1(e10,e12) = e12 )
& ( op1(e10,e13) = e13 )
& ( op1(e11,e10) = e11 )
& ( op1(e11,e11) = e10 )
& ( op1(e11,e12) = e13 )
& ( op1(e11,e13) = e12 )
& ( op1(e12,e10) = e12 )
& ( op1(e12,e11) = e13 )
& ( op1(e12,e12) = e10 )
& ( op1(e12,e13) = e11 )
& ( op1(e13,e10) = e13 )
& ( op1(e13,e11) = e12 )
& ( op1(e13,e12) = e11 )
& ( op1(e13,e13) = e10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
tff(c_20,plain,
e23 != e20,
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_90,plain,
op2(e23,e23) = e20,
inference(cnfTransformation,[status(thm)],[f_168]) ).
tff(c_100,plain,
op2(e22,e22) = e23,
inference(cnfTransformation,[status(thm)],[f_168]) ).
tff(c_110,plain,
op2(e21,e21) = e23,
inference(cnfTransformation,[status(thm)],[f_168]) ).
tff(c_208,plain,
( ( j(e20) = e13 )
| ( j(e20) = e12 )
| ( j(e20) = e11 )
| ( j(e20) = e10 ) ),
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_413,plain,
j(e20) = e10,
inference(splitLeft,[status(thm)],[c_208]) ).
tff(c_136,plain,
h(j(e20)) = e20,
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_414,plain,
h(e10) = e20,
inference(demodulation,[status(thm),theory(equality)],[c_413,c_136]) ).
tff(c_68,plain,
op1(e12,e12) = e10,
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_202,plain,
( ( j(e23) = e13 )
| ( j(e23) = e12 )
| ( j(e23) = e11 )
| ( j(e23) = e10 ) ),
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_637,plain,
j(e23) = e10,
inference(splitLeft,[status(thm)],[c_202]) ).
tff(c_130,plain,
h(j(e23)) = e23,
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_661,plain,
h(e10) = e23,
inference(demodulation,[status(thm),theory(equality)],[c_637,c_130]) ).
tff(c_665,plain,
e23 = e20,
inference(demodulation,[status(thm),theory(equality)],[c_414,c_661]) ).
tff(c_667,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_20,c_665]) ).
tff(c_669,plain,
j(e23) != e10,
inference(splitRight,[status(thm)],[c_202]) ).
tff(c_78,plain,
op1(e11,e11) = e10,
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_58,plain,
op1(e13,e13) = e10,
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_24,plain,
e21 != e20,
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_206,plain,
( ( j(e21) = e13 )
| ( j(e21) = e12 )
| ( j(e21) = e11 )
| ( j(e21) = e10 ) ),
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_580,plain,
j(e21) = e10,
inference(splitLeft,[status(thm)],[c_206]) ).
tff(c_134,plain,
h(j(e21)) = e21,
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_588,plain,
h(e10) = e21,
inference(demodulation,[status(thm),theory(equality)],[c_580,c_134]) ).
tff(c_590,plain,
e21 = e20,
inference(demodulation,[status(thm),theory(equality)],[c_414,c_588]) ).
tff(c_592,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_24,c_590]) ).
tff(c_593,plain,
( ( j(e21) = e11 )
| ( j(e21) = e12 )
| ( j(e21) = e13 ) ),
inference(splitRight,[status(thm)],[c_206]) ).
tff(c_604,plain,
j(e21) = e13,
inference(splitLeft,[status(thm)],[c_593]) ).
tff(c_158,plain,
op1(j(e21),j(e21)) = j(op2(e21,e21)),
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_222,plain,
op1(j(e21),j(e21)) = j(e23),
inference(demodulation,[status(thm),theory(equality)],[c_110,c_158]) ).
tff(c_606,plain,
op1(e13,e13) = j(e23),
inference(demodulation,[status(thm),theory(equality)],[c_604,c_604,c_222]) ).
tff(c_617,plain,
j(e23) = e10,
inference(demodulation,[status(thm),theory(equality)],[c_58,c_606]) ).
tff(c_627,plain,
h(e10) = e23,
inference(demodulation,[status(thm),theory(equality)],[c_617,c_130]) ).
tff(c_631,plain,
e23 = e20,
inference(demodulation,[status(thm),theory(equality)],[c_414,c_627]) ).
tff(c_633,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_20,c_631]) ).
tff(c_634,plain,
( ( j(e21) = e12 )
| ( j(e21) = e11 ) ),
inference(splitRight,[status(thm)],[c_593]) ).
tff(c_636,plain,
j(e21) = e11,
inference(splitLeft,[status(thm)],[c_634]) ).
tff(c_672,plain,
op1(e11,e11) = j(e23),
inference(demodulation,[status(thm),theory(equality)],[c_636,c_636,c_222]) ).
tff(c_683,plain,
j(e23) = e10,
inference(demodulation,[status(thm),theory(equality)],[c_78,c_672]) ).
tff(c_689,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_669,c_683]) ).
tff(c_690,plain,
j(e21) = e12,
inference(splitRight,[status(thm)],[c_634]) ).
tff(c_694,plain,
op1(e12,e12) = j(e23),
inference(demodulation,[status(thm),theory(equality)],[c_690,c_690,c_222]) ).
tff(c_705,plain,
j(e23) = e10,
inference(demodulation,[status(thm),theory(equality)],[c_68,c_694]) ).
tff(c_716,plain,
h(e10) = e23,
inference(demodulation,[status(thm),theory(equality)],[c_705,c_130]) ).
tff(c_720,plain,
e23 = e20,
inference(demodulation,[status(thm),theory(equality)],[c_414,c_716]) ).
tff(c_722,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_20,c_720]) ).
tff(c_724,plain,
j(e20) != e10,
inference(splitRight,[status(thm)],[c_208]) ).
tff(c_216,plain,
( ( h(e10) = e23 )
| ( h(e10) = e22 )
| ( h(e10) = e21 )
| ( h(e10) = e20 ) ),
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_1021,plain,
h(e10) = e20,
inference(splitLeft,[status(thm)],[c_216]) ).
tff(c_128,plain,
j(h(e10)) = e10,
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_1029,plain,
j(e20) = e10,
inference(demodulation,[status(thm),theory(equality)],[c_1021,c_128]) ).
tff(c_1032,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_724,c_1029]) ).
tff(c_1034,plain,
h(e10) != e20,
inference(splitRight,[status(thm)],[c_216]) ).
tff(c_120,plain,
op2(e20,e20) = e20,
inference(cnfTransformation,[status(thm)],[f_168]) ).
tff(c_212,plain,
( ( h(e12) = e23 )
| ( h(e12) = e22 )
| ( h(e12) = e21 )
| ( h(e12) = e20 ) ),
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_1063,plain,
h(e12) = e20,
inference(splitLeft,[status(thm)],[c_212]) ).
tff(c_180,plain,
op2(h(e12),h(e12)) = h(op1(e12,e12)),
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_243,plain,
op2(h(e12),h(e12)) = h(e10),
inference(demodulation,[status(thm),theory(equality)],[c_68,c_180]) ).
tff(c_1072,plain,
op2(e20,e20) = h(e10),
inference(demodulation,[status(thm),theory(equality)],[c_1063,c_1063,c_243]) ).
tff(c_1074,plain,
h(e10) = e20,
inference(demodulation,[status(thm),theory(equality)],[c_120,c_1072]) ).
tff(c_1076,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1034,c_1074]) ).
tff(c_1077,plain,
( ( h(e12) = e21 )
| ( h(e12) = e22 )
| ( h(e12) = e23 ) ),
inference(splitRight,[status(thm)],[c_212]) ).
tff(c_1083,plain,
h(e12) = e23,
inference(splitLeft,[status(thm)],[c_1077]) ).
tff(c_1093,plain,
op2(e23,e23) = h(e10),
inference(demodulation,[status(thm),theory(equality)],[c_1083,c_1083,c_243]) ).
tff(c_1095,plain,
h(e10) = e20,
inference(demodulation,[status(thm),theory(equality)],[c_90,c_1093]) ).
tff(c_1097,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1034,c_1095]) ).
tff(c_1098,plain,
( ( h(e12) = e22 )
| ( h(e12) = e21 ) ),
inference(splitRight,[status(thm)],[c_1077]) ).
tff(c_1100,plain,
h(e12) = e21,
inference(splitLeft,[status(thm)],[c_1098]) ).
tff(c_1111,plain,
op2(e21,e21) = h(e10),
inference(demodulation,[status(thm),theory(equality)],[c_1100,c_1100,c_243]) ).
tff(c_1113,plain,
h(e10) = e23,
inference(demodulation,[status(thm),theory(equality)],[c_110,c_1111]) ).
tff(c_88,plain,
op1(e10,e10) = e10,
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_200,plain,
op2(h(e10),h(e10)) = h(op1(e10,e10)),
inference(cnfTransformation,[status(thm)],[f_313]) ).
tff(c_233,plain,
op2(h(e10),h(e10)) = h(e10),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_200]) ).
tff(c_1123,plain,
op2(e23,e23) = e23,
inference(demodulation,[status(thm),theory(equality)],[c_1113,c_1113,c_1113,c_233]) ).
tff(c_1127,plain,
e23 = e20,
inference(demodulation,[status(thm),theory(equality)],[c_90,c_1123]) ).
tff(c_1129,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_20,c_1127]) ).
tff(c_1130,plain,
h(e12) = e22,
inference(splitRight,[status(thm)],[c_1098]) ).
tff(c_1144,plain,
op2(e22,e22) = h(e10),
inference(demodulation,[status(thm),theory(equality)],[c_1130,c_1130,c_243]) ).
tff(c_1146,plain,
h(e10) = e23,
inference(demodulation,[status(thm),theory(equality)],[c_100,c_1144]) ).
tff(c_1156,plain,
op2(e23,e23) = e23,
inference(demodulation,[status(thm),theory(equality)],[c_1146,c_1146,c_1146,c_233]) ).
tff(c_1160,plain,
e23 = e20,
inference(demodulation,[status(thm),theory(equality)],[c_90,c_1156]) ).
tff(c_1162,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_20,c_1160]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ALG042+1 : TPTP v9.0.0. Released v2.7.0.
% 0.07/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.35 % Computer : n015.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 : Sun Apr 6 06:56:20 EDT 2025
% 0.13/0.35 % CPUTime :
% 5.82/2.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.10/2.29
% 6.10/2.29 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------