TSTP Solution File: GRP668-1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP668-1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n002.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 : Thu Aug 31 00:22:58 EDT 2023
% Result : Unsatisfiable 2.50s 2.55s
% Output : CNFRefutation 2.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 16
% Syntax : Number of formulae : 98 ( 91 unt; 7 typ; 0 def)
% Number of atoms : 91 ( 90 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 188 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
ld: ( $i * $i ) > $i ).
tff(decl_23,type,
mult: ( $i * $i ) > $i ).
tff(decl_24,type,
rd: ( $i * $i ) > $i ).
tff(decl_25,type,
unit: $i ).
tff(decl_26,type,
a: $i ).
tff(decl_27,type,
b: $i ).
tff(decl_28,type,
c: $i ).
cnf(c05,axiom,
mult(X1,unit) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c05) ).
cnf(c07,axiom,
mult(X1,mult(X2,mult(X2,X3))) = mult(mult(mult(X1,X2),X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c07) ).
cnf(c06,axiom,
mult(unit,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c06) ).
cnf(c02,axiom,
ld(X1,mult(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c02) ).
cnf(c08,axiom,
mult(mult(X1,X2),X1) = mult(X1,mult(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c08) ).
cnf(c01,axiom,
mult(X1,ld(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c01) ).
cnf(c04,axiom,
rd(mult(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c04) ).
cnf(c03,axiom,
mult(rd(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c03) ).
cnf(goals,negated_conjecture,
mult(mult(a,b),mult(mult(c,b),c)) != mult(mult(a,mult(mult(b,c),b)),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(c_0_9,axiom,
mult(X1,unit) = X1,
c05 ).
cnf(c_0_10,axiom,
mult(X1,mult(X2,mult(X2,X3))) = mult(mult(mult(X1,X2),X2),X3),
c07 ).
cnf(c_0_11,plain,
mult(mult(X1,X2),X2) = mult(X1,mult(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_9]) ).
cnf(c_0_12,plain,
mult(mult(X1,mult(X2,X2)),X3) = mult(X1,mult(X2,mult(X2,X3))),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_13,axiom,
mult(unit,X1) = X1,
c06 ).
cnf(c_0_14,axiom,
ld(X1,mult(X1,X2)) = X2,
c02 ).
cnf(c_0_15,plain,
mult(mult(X1,X1),X2) = mult(X1,mult(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_13]) ).
cnf(c_0_16,axiom,
mult(mult(X1,X2),X1) = mult(X1,mult(X2,X1)),
c08 ).
cnf(c_0_17,axiom,
mult(X1,ld(X1,X2)) = X2,
c01 ).
cnf(c_0_18,plain,
ld(mult(X1,X1),mult(X1,mult(X1,X2))) = X2,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
mult(X1,mult(ld(X1,X2),X1)) = mult(X2,X1),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
ld(mult(X1,X1),mult(X1,X2)) = ld(X1,X2),
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_21,plain,
mult(ld(X1,X2),X1) = ld(X1,mult(X2,X1)),
inference(spm,[status(thm)],[c_0_14,c_0_19]) ).
cnf(c_0_22,plain,
ld(mult(X1,X1),X1) = ld(X1,unit),
inference(spm,[status(thm)],[c_0_20,c_0_9]) ).
cnf(c_0_23,axiom,
rd(mult(X1,X2),X2) = X1,
c04 ).
cnf(c_0_24,axiom,
mult(rd(X1,X2),X2) = X1,
c03 ).
cnf(c_0_25,plain,
mult(ld(X1,unit),mult(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_20]),c_0_14]) ).
cnf(c_0_26,plain,
rd(mult(X1,mult(X2,mult(X2,X3))),X3) = mult(X1,mult(X2,X2)),
inference(spm,[status(thm)],[c_0_23,c_0_12]) ).
cnf(c_0_27,plain,
mult(rd(X1,X2),mult(X2,X2)) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_11,c_0_24]) ).
cnf(c_0_28,plain,
mult(ld(X1,unit),mult(X1,mult(X1,X2))) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_12,c_0_25]) ).
cnf(c_0_29,plain,
rd(mult(X1,mult(X2,X3)),ld(X2,X3)) = mult(X1,mult(X2,X2)),
inference(spm,[status(thm)],[c_0_26,c_0_17]) ).
cnf(c_0_30,plain,
ld(rd(X1,X2),mult(X1,X2)) = mult(X2,X2),
inference(spm,[status(thm)],[c_0_14,c_0_27]) ).
cnf(c_0_31,plain,
mult(ld(X1,unit),mult(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_28,c_0_17]) ).
cnf(c_0_32,plain,
ld(rd(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_14,c_0_24]) ).
cnf(c_0_33,plain,
rd(mult(X1,X2),ld(X2,unit)) = mult(X1,mult(X2,X2)),
inference(spm,[status(thm)],[c_0_29,c_0_9]) ).
cnf(c_0_34,plain,
rd(X1,ld(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_23,c_0_17]) ).
cnf(c_0_35,plain,
ld(rd(unit,X1),X1) = mult(X1,X1),
inference(spm,[status(thm)],[c_0_30,c_0_13]) ).
cnf(c_0_36,plain,
rd(X1,mult(X2,X1)) = ld(X2,unit),
inference(spm,[status(thm)],[c_0_23,c_0_31]) ).
cnf(c_0_37,plain,
mult(X1,mult(ld(X1,X2),ld(X1,X2))) = mult(X2,ld(X1,X2)),
inference(spm,[status(thm)],[c_0_11,c_0_17]) ).
cnf(c_0_38,plain,
ld(mult(X1,mult(X2,X2)),mult(X1,X2)) = ld(X2,unit),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,plain,
mult(ld(X1,unit),X2) = ld(X1,X2),
inference(spm,[status(thm)],[c_0_31,c_0_17]) ).
cnf(c_0_40,plain,
rd(X1,mult(X1,X1)) = rd(unit,X1),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,plain,
rd(mult(X1,mult(X2,X2)),X2) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_23,c_0_11]) ).
cnf(c_0_42,plain,
ld(ld(X1,unit),X2) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_14,c_0_31]) ).
cnf(c_0_43,plain,
ld(rd(X1,X2),unit) = rd(X2,X1),
inference(spm,[status(thm)],[c_0_36,c_0_24]) ).
cnf(c_0_44,plain,
mult(mult(X1,X2),ld(X2,unit)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_12]),c_0_17]),c_0_17]),c_0_9]) ).
cnf(c_0_45,plain,
rd(unit,X1) = ld(X1,unit),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_25]),c_0_40]) ).
cnf(c_0_46,plain,
mult(rd(X1,mult(X2,X2)),X2) = rd(X1,X2),
inference(spm,[status(thm)],[c_0_41,c_0_24]) ).
cnf(c_0_47,plain,
mult(rd(X1,X2),X3) = ld(rd(X2,X1),X3),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_48,plain,
mult(mult(X1,X2),mult(X1,X2)) = mult(X1,mult(X2,mult(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_36]),c_0_42]) ).
cnf(c_0_49,plain,
mult(X1,mult(X1,ld(mult(X1,X1),X2))) = X2,
inference(spm,[status(thm)],[c_0_17,c_0_15]) ).
cnf(c_0_50,plain,
mult(mult(X1,ld(X2,unit)),X2) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_32]),c_0_45]) ).
cnf(c_0_51,plain,
ld(rd(mult(X1,X1),X2),X1) = rd(X2,X1),
inference(rw,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,plain,
ld(mult(X1,X2),X1) = ld(X2,unit),
inference(spm,[status(thm)],[c_0_14,c_0_44]) ).
cnf(c_0_53,plain,
mult(mult(X1,X2),ld(X2,X1)) = mult(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_44]),c_0_39]) ).
cnf(c_0_54,plain,
mult(X1,ld(mult(X1,X1),X2)) = ld(X1,X2),
inference(spm,[status(thm)],[c_0_14,c_0_49]) ).
cnf(c_0_55,plain,
mult(X1,ld(X2,unit)) = rd(X1,X2),
inference(spm,[status(thm)],[c_0_23,c_0_50]) ).
cnf(c_0_56,plain,
rd(mult(X1,X1),X2) = rd(X1,rd(X2,X1)),
inference(spm,[status(thm)],[c_0_34,c_0_51]) ).
cnf(c_0_57,plain,
ld(ld(X1,X2),unit) = ld(X2,X1),
inference(spm,[status(thm)],[c_0_52,c_0_17]) ).
cnf(c_0_58,plain,
mult(mult(X1,rd(X1,X2)),X2) = mult(X1,X1),
inference(spm,[status(thm)],[c_0_53,c_0_32]) ).
cnf(c_0_59,plain,
ld(mult(X1,X1),X2) = ld(X1,ld(X1,X2)),
inference(spm,[status(thm)],[c_0_14,c_0_54]) ).
cnf(c_0_60,plain,
rd(X1,ld(X2,unit)) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_34,c_0_52]) ).
cnf(c_0_61,plain,
mult(X1,rd(X2,X3)) = rd(X1,rd(X3,X2)),
inference(spm,[status(thm)],[c_0_55,c_0_43]) ).
cnf(c_0_62,plain,
rd(rd(X1,X2),X2) = rd(X1,mult(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_56]),c_0_43]) ).
cnf(c_0_63,plain,
mult(ld(X1,mult(X2,X2)),X3) = ld(X1,mult(X2,mult(X2,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_39]),c_0_39]) ).
cnf(c_0_64,plain,
mult(ld(X1,X2),X3) = ld(ld(X2,X1),X3),
inference(spm,[status(thm)],[c_0_42,c_0_57]) ).
cnf(c_0_65,plain,
ld(X1,rd(X1,X2)) = ld(X2,unit),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_58]),c_0_59]),c_0_14]) ).
cnf(c_0_66,plain,
ld(rd(rd(X1,mult(X2,X2)),X3),X1) = mult(X3,mult(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_60]),c_0_55]),c_0_61]),c_0_61]),c_0_62]),c_0_47]) ).
cnf(c_0_67,plain,
ld(ld(X1,ld(X1,X2)),X3) = ld(X2,mult(X1,mult(X1,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64]),c_0_59]) ).
cnf(c_0_68,plain,
mult(X1,mult(X2,mult(X2,ld(mult(X1,mult(X2,X2)),X3)))) = X3,
inference(spm,[status(thm)],[c_0_17,c_0_12]) ).
cnf(c_0_69,plain,
mult(X1,ld(X2,X3)) = rd(X1,ld(X3,X2)),
inference(spm,[status(thm)],[c_0_60,c_0_57]) ).
cnf(c_0_70,plain,
rd(ld(X1,mult(X2,X2)),X2) = ld(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_39]),c_0_39]) ).
cnf(c_0_71,plain,
ld(mult(X1,X2),unit) = ld(X2,ld(X1,unit)),
inference(spm,[status(thm)],[c_0_65,c_0_36]) ).
cnf(c_0_72,plain,
ld(rd(X1,X2),mult(X1,mult(X3,X3))) = mult(X2,mult(X3,X3)),
inference(spm,[status(thm)],[c_0_66,c_0_23]) ).
cnf(c_0_73,plain,
ld(mult(X1,X2),mult(X1,mult(X1,X3))) = ld(ld(X1,X2),X3),
inference(spm,[status(thm)],[c_0_67,c_0_14]) ).
cnf(c_0_74,plain,
rd(X1,rd(ld(X2,mult(X3,mult(X1,X1))),X1)) = ld(X3,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_68]),c_0_69]),c_0_61]) ).
cnf(c_0_75,plain,
rd(ld(X1,unit),X2) = ld(X1,ld(X2,unit)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_52]),c_0_15]),c_0_52]),c_0_71]) ).
cnf(c_0_76,plain,
ld(mult(X1,X2),mult(X1,mult(X3,X3))) = ld(X2,mult(X3,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_60]),c_0_39]) ).
cnf(c_0_77,plain,
ld(mult(X1,X2),mult(X1,X3)) = ld(ld(X1,X2),ld(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_68]),c_0_69]),c_0_61]),c_0_74]) ).
cnf(c_0_78,plain,
rd(X1,ld(X2,ld(X3,unit))) = mult(X1,mult(X3,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_60]),c_0_75]) ).
cnf(c_0_79,plain,
ld(ld(X1,X2),ld(X1,mult(X3,X3))) = ld(X2,mult(X3,X3)),
inference(rw,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_80,plain,
ld(X1,X1) = unit,
inference(spm,[status(thm)],[c_0_14,c_0_9]) ).
cnf(c_0_81,negated_conjecture,
mult(mult(a,b),mult(mult(c,b),c)) != mult(mult(a,mult(mult(b,c),b)),c),
goals ).
cnf(c_0_82,plain,
ld(rd(rd(X1,X2),X3),mult(X1,X2)) = mult(X3,mult(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_78]),c_0_55]),c_0_61]),c_0_47]) ).
cnf(c_0_83,plain,
ld(ld(X1,ld(X2,unit)),X3) = mult(mult(X2,X1),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_60]),c_0_75]) ).
cnf(c_0_84,plain,
ld(ld(mult(X1,X2),X3),ld(X2,X1)) = ld(X3,mult(X1,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_77]),c_0_80]),c_0_57]) ).
cnf(c_0_85,negated_conjecture,
mult(mult(a,mult(b,mult(c,b))),c) != mult(mult(a,b),mult(c,mult(b,c))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_16]),c_0_16]) ).
cnf(c_0_86,plain,
mult(mult(X1,X2),mult(X3,mult(X2,X3))) = mult(X1,mult(X2,mult(X3,mult(X2,X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_36]),c_0_75]),c_0_83]),c_0_48]) ).
cnf(c_0_87,plain,
ld(ld(mult(X1,mult(X2,X1)),X3),X2) = ld(X3,mult(X1,mult(X2,mult(X1,X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_14]),c_0_16]),c_0_48]) ).
cnf(c_0_88,negated_conjecture,
mult(mult(a,mult(b,mult(c,b))),c) != mult(a,mult(b,mult(c,mult(b,c)))),
inference(rw,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_89,plain,
mult(mult(X1,mult(X2,mult(X3,X2))),X3) = mult(X1,mult(X2,mult(X3,mult(X2,X3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_87]),c_0_42]) ).
cnf(c_0_90,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_89])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP668-1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 22:40:49 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.62 start to proof: theBenchmark
% 2.50/2.55 % Version : CSE_E---1.5
% 2.50/2.55 % Problem : theBenchmark.p
% 2.50/2.55 % Proof found
% 2.50/2.55 % SZS status Theorem for theBenchmark.p
% 2.50/2.55 % SZS output start Proof
% See solution above
% 2.50/2.56 % Total time : 1.924000 s
% 2.50/2.56 % SZS output end Proof
% 2.50/2.56 % Total time : 1.927000 s
%------------------------------------------------------------------------------