%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP697-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:31:13 AM UTC 2026
% Result : Unsatisfiable 2.16s 0.73s
% Output : CNFRefutation 2.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 10
% Syntax : Number of formulae : 86 ( 86 unt; 0 def)
% Number of atoms : 86 ( 85 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 148 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(c02,axiom,
! [VAR_0,VAR_1] : ld(VAR_0,mult(VAR_0,VAR_1)) = VAR_1,
file('theBenchmark.p',c02) ).
cnf(c_2,plain,
ld(A,mult(A,B)) = B,
inference(clausify,[status(thm)],[c02]) ).
fof(c03,axiom,
! [VAR_0,VAR_1] : mult(rd(VAR_0,VAR_1),VAR_1) = VAR_0,
file('theBenchmark.p',c03) ).
cnf(c_3,plain,
mult(rd(A,B),B) = A,
inference(clausify,[status(thm)],[c03]) ).
fof(c05,axiom,
! [VAR_0] : mult(VAR_0,unit) = VAR_0,
file('theBenchmark.p',c05) ).
cnf(c_5,plain,
mult(A,unit) = A,
inference(clausify,[status(thm)],[c05]) ).
fof(c06,axiom,
! [VAR_0] : mult(unit,VAR_0) = VAR_0,
file('theBenchmark.p',c06) ).
cnf(c_6,plain,
mult(unit,A) = A,
inference(clausify,[status(thm)],[c06]) ).
fof(c07,axiom,
! [VAR_0,VAR_1] : mult(VAR_0,i(mult(VAR_1,VAR_0))) = i(VAR_1),
file('theBenchmark.p',c07) ).
cnf(c_7,plain,
mult(A,i(mult(B,A))) = i(B),
inference(clausify,[status(thm)],[c07]) ).
fof(c08,axiom,
! [VAR_0,VAR_1,VAR_2] : mult(VAR_0,mult(VAR_1,VAR_2)) = mult(rd(mult(VAR_0,VAR_1),VAR_0),mult(VAR_0,VAR_2)),
file('theBenchmark.p',c08) ).
cnf(c_8,plain,
mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)),
inference(clausify,[status(thm)],[c08]) ).
cnf(c_9,plain,
mult(rd(mult(A,B),A),mult(A,C)) = mult(A,mult(B,C)),
inference(copy,[status(thm)],[c_8]) ).
fof(c09,axiom,
! [VAR_0,VAR_1,VAR_2] : mult(mult(VAR_0,VAR_1),VAR_2) = mult(mult(VAR_0,VAR_2),ld(VAR_2,mult(VAR_1,VAR_2))),
file('theBenchmark.p',c09) ).
cnf(c_10,plain,
mult(mult(A,B),C) = mult(mult(A,C),ld(C,mult(B,C))),
inference(clausify,[status(thm)],[c09]) ).
cnf(c_11,plain,
mult(mult(A,B),ld(B,mult(C,B))) = mult(mult(A,C),B),
inference(copy,[status(thm)],[c_10]) ).
fof(c10,axiom,
! [VAR_0] : mult(i(VAR_0),VAR_0) = unit,
file('theBenchmark.p',c10) ).
cnf(c_12,plain,
mult(i(A),A) = unit,
inference(clausify,[status(thm)],[c10]) ).
fof(c11,axiom,
! [VAR_0] : mult(VAR_0,i(VAR_0)) = unit,
file('theBenchmark.p',c11) ).
cnf(c_13,plain,
mult(A,i(A)) = unit,
inference(clausify,[status(thm)],[c11]) ).
fof(goals,axiom,
mult(mult(a,b),mult(b,mult(c,b))) != mult(mult(a,mult(b,mult(b,c))),b),
file('theBenchmark.p',goals) ).
cnf(c_14,plain,
mult(mult(a,b),mult(b,mult(c,b))) != mult(mult(a,mult(b,mult(b,c))),b),
inference(clausify,[status(thm)],[goals]) ).
cnf(c_15,plain,
mult(mult(a,mult(b,mult(b,c))),b) != mult(mult(a,b),mult(b,mult(c,b))),
inference(copy,[status(thm)],[c_14]) ).
cnf(c_659,plain,
mult(A,i(B)) = i(rd(B,A)),
inference(paramod,[status(thm)],[c_3,c_7]) ).
cnf(c_24,plain,
i(rd(A,B)) = mult(B,i(A)),
inference(copy,[status(thm)],[c_659]) ).
cnf(c_660,plain,
mult(A,i(A)) = i(unit),
inference(paramod,[status(thm)],[c_6,c_7]) ).
cnf(c_661,plain,
unit = i(unit),
inference(paramod,[status(thm)],[c_13,c_660]) ).
cnf(c_26,plain,
i(unit) = unit,
inference(copy,[status(thm)],[c_661]) ).
cnf(c_27,plain,
mult(i(mult(A,B)),i(i(A))) = i(B),
inference(paramod,[status(thm)],[c_7,c_7]) ).
cnf(c_662,plain,
mult(mult(A,B),i(mult(A,mult(C,B)))) = i(rd(mult(A,C),A)),
inference(paramod,[status(thm)],[c_9,c_7]) ).
cnf(c_33,plain,
mult(mult(A,B),i(mult(A,mult(C,B)))) = mult(A,i(mult(A,C))),
inference(paramod,[status(thm)],[c_24,c_662]) ).
cnf(c_50,plain,
mult(i(A),ld(i(mult(A,B)),mult(C,i(mult(A,B))))) = mult(mult(B,C),i(mult(A,B))),
inference(paramod,[status(thm)],[c_7,c_11]) ).
cnf(c_663,plain,
mult(A,i(unit)) = i(i(A)),
inference(paramod,[status(thm)],[c_12,c_7]) ).
cnf(c_664,plain,
mult(A,unit) = i(i(A)),
inference(paramod,[status(thm)],[c_26,c_663]) ).
cnf(c_665,plain,
A = i(i(A)),
inference(paramod,[status(thm)],[c_5,c_664]) ).
cnf(c_61,plain,
i(i(A)) = A,
inference(copy,[status(thm)],[c_665]) ).
cnf(c_666,plain,
mult(unit,ld(A,mult(B,A))) = mult(mult(i(A),B),A),
inference(paramod,[status(thm)],[c_12,c_11]) ).
cnf(c_62,plain,
ld(A,mult(B,A)) = mult(mult(i(A),B),A),
inference(paramod,[status(thm)],[c_6,c_666]) ).
cnf(c_667,plain,
mult(mult(A,B),ld(B,unit)) = mult(mult(A,i(B)),B),
inference(paramod,[status(thm)],[c_12,c_11]) ).
cnf(c_63,plain,
mult(mult(A,i(B)),B) = mult(mult(A,B),ld(B,unit)),
inference(copy,[status(thm)],[c_667]) ).
cnf(c_668,plain,
mult(mult(i(A),B),ld(B,mult(A,B))) = mult(unit,B),
inference(paramod,[status(thm)],[c_12,c_11]) ).
cnf(c_669,plain,
mult(mult(i(A),B),mult(mult(i(B),A),B)) = mult(unit,B),
inference(paramod,[status(thm)],[c_62,c_668]) ).
cnf(c_64,plain,
mult(mult(i(A),B),mult(mult(i(B),A),B)) = B,
inference(paramod,[status(thm)],[c_6,c_669]) ).
cnf(c_65,plain,
mult(i(mult(A,B)),A) = i(B),
inference(paramod,[status(thm)],[c_61,c_27]) ).
cnf(c_670,plain,
mult(i(A),mult(mult(i(i(mult(A,B))),C),i(mult(A,B)))) = mult(mult(B,C),i(mult(A,B))),
inference(paramod,[status(thm)],[c_62,c_50]) ).
cnf(c_71,plain,
mult(i(A),mult(mult(mult(A,B),C),i(mult(A,B)))) = mult(mult(B,C),i(mult(A,B))),
inference(paramod,[status(thm)],[c_61,c_670]) ).
cnf(c_84,plain,
mult(mult(A,B),mult(mult(i(B),C),B)) = mult(mult(A,C),B),
inference(paramod,[status(thm)],[c_62,c_11]) ).
cnf(c_85,plain,
ld(A,unit) = i(A),
inference(paramod,[status(thm)],[c_13,c_2]) ).
cnf(c_86,plain,
mult(mult(A,i(B)),B) = mult(mult(A,B),i(B)),
inference(paramod,[status(thm)],[c_85,c_63]) ).
cnf(c_671,plain,
mult(mult(A,i(B)),i(mult(A,unit))) = mult(A,i(mult(A,B))),
inference(paramod,[status(thm)],[c_13,c_33]) ).
cnf(c_672,plain,
mult(mult(A,i(B)),i(A)) = mult(A,i(mult(A,B))),
inference(paramod,[status(thm)],[c_5,c_671]) ).
cnf(c_127,plain,
mult(A,i(mult(A,B))) = mult(mult(A,i(B)),i(A)),
inference(copy,[status(thm)],[c_672]) ).
cnf(c_673,plain,
mult(i(A),mult(i(B),A)) = i(mult(mult(i(A),B),A)),
inference(paramod,[status(thm)],[c_64,c_65]) ).
cnf(c_149,plain,
i(mult(mult(i(A),B),A)) = mult(i(A),mult(i(B),A)),
inference(copy,[status(thm)],[c_673]) ).
cnf(c_674,plain,
mult(A,i(i(B))) = mult(mult(A,i(i(mult(B,A)))),i(A)),
inference(paramod,[status(thm)],[c_7,c_127]) ).
cnf(c_675,plain,
mult(A,B) = mult(mult(A,i(i(mult(B,A)))),i(A)),
inference(paramod,[status(thm)],[c_61,c_674]) ).
cnf(c_676,plain,
mult(A,B) = mult(mult(A,mult(B,A)),i(A)),
inference(paramod,[status(thm)],[c_61,c_675]) ).
cnf(c_174,plain,
mult(mult(A,mult(B,A)),i(A)) = mult(A,B),
inference(copy,[status(thm)],[c_676]) ).
cnf(c_677,plain,
mult(i(A),i(mult(A,B))) = i(mult(A,mult(B,A))),
inference(paramod,[status(thm)],[c_174,c_7]) ).
cnf(c_270,plain,
i(mult(A,mult(B,A))) = mult(i(A),i(mult(A,B))),
inference(copy,[status(thm)],[c_677]) ).
cnf(c_678,plain,
mult(mult(i(A),mult(A,B)),i(i(A))) = mult(i(A),mult(A,mult(B,A))),
inference(paramod,[status(thm)],[c_174,c_174]) ).
cnf(c_282,plain,
mult(mult(i(A),mult(A,B)),A) = mult(i(A),mult(A,mult(B,A))),
inference(paramod,[status(thm)],[c_61,c_678]) ).
cnf(c_679,plain,
mult(mult(i(A),i(mult(A,B))),A) = i(mult(B,A)),
inference(paramod,[status(thm)],[c_270,c_65]) ).
cnf(c_290,plain,
i(mult(A,B)) = mult(mult(i(B),i(mult(B,A))),B),
inference(copy,[status(thm)],[c_679]) ).
cnf(c_680,plain,
mult(i(A),mult(mult(A,B),i(mult(A,unit)))) = mult(mult(unit,B),i(mult(A,unit))),
inference(paramod,[status(thm)],[c_5,c_71]) ).
cnf(c_681,plain,
mult(i(A),mult(mult(A,B),i(A))) = mult(mult(unit,B),i(mult(A,unit))),
inference(paramod,[status(thm)],[c_5,c_680]) ).
cnf(c_682,plain,
mult(i(A),mult(mult(A,B),i(A))) = mult(B,i(mult(A,unit))),
inference(paramod,[status(thm)],[c_6,c_681]) ).
cnf(c_353,plain,
mult(i(A),mult(mult(A,B),i(A))) = mult(B,i(A)),
inference(paramod,[status(thm)],[c_5,c_682]) ).
cnf(c_683,plain,
i(mult(mult(i(A),i(mult(A,B))),A)) = mult(B,A),
inference(paramod,[status(thm)],[c_290,c_61]) ).
cnf(c_684,plain,
mult(i(A),mult(i(i(mult(A,B))),A)) = mult(B,A),
inference(paramod,[status(thm)],[c_149,c_683]) ).
cnf(c_415,plain,
mult(i(A),mult(mult(A,B),A)) = mult(B,A),
inference(paramod,[status(thm)],[c_61,c_684]) ).
cnf(c_685,plain,
mult(mult(A,i(B)),i(i(B))) = mult(i(B),mult(B,A)),
inference(paramod,[status(thm)],[c_353,c_174]) ).
cnf(c_686,plain,
mult(mult(A,i(B)),B) = mult(i(B),mult(B,A)),
inference(paramod,[status(thm)],[c_61,c_685]) ).
cnf(c_687,plain,
mult(mult(A,B),i(B)) = mult(i(B),mult(B,A)),
inference(paramod,[status(thm)],[c_86,c_686]) ).
cnf(c_570,plain,
mult(i(A),mult(A,B)) = mult(mult(B,A),i(A)),
inference(copy,[status(thm)],[c_687]) ).
cnf(c_688,plain,
mult(i(i(A)),mult(mult(B,A),i(i(A)))) = mult(mult(mult(A,B),A),i(i(A))),
inference(paramod,[status(thm)],[c_415,c_353]) ).
cnf(c_689,plain,
mult(A,mult(mult(B,A),i(i(A)))) = mult(mult(mult(A,B),A),i(i(A))),
inference(paramod,[status(thm)],[c_61,c_688]) ).
cnf(c_690,plain,
mult(A,mult(mult(B,A),A)) = mult(mult(mult(A,B),A),i(i(A))),
inference(paramod,[status(thm)],[c_61,c_689]) ).
cnf(c_691,plain,
mult(A,mult(mult(B,A),A)) = mult(mult(mult(A,B),A),A),
inference(paramod,[status(thm)],[c_61,c_690]) ).
cnf(c_573,plain,
mult(mult(mult(A,B),A),A) = mult(A,mult(mult(B,A),A)),
inference(copy,[status(thm)],[c_691]) ).
cnf(c_692,plain,
mult(mult(a,b),mult(mult(i(b),mult(b,mult(b,c))),b)) != mult(mult(a,b),mult(b,mult(c,b))),
inference(paramod,[status(thm)],[c_84,c_15]) ).
cnf(c_578,plain,
mult(mult(a,b),mult(i(b),mult(b,mult(mult(b,c),b)))) != mult(mult(a,b),mult(b,mult(c,b))),
inference(paramod,[status(thm)],[c_282,c_692]) ).
cnf(c_693,plain,
mult(mult(a,b),mult(mult(mult(mult(b,c),b),b),i(b))) != mult(mult(a,b),mult(b,mult(c,b))),
inference(paramod,[status(thm)],[c_570,c_578]) ).
cnf(c_694,plain,
mult(mult(a,b),mult(mult(b,mult(mult(c,b),b)),i(b))) != mult(mult(a,b),mult(b,mult(c,b))),
inference(paramod,[status(thm)],[c_573,c_693]) ).
cnf(c_695,plain,
mult(mult(a,b),mult(b,mult(c,b))) != mult(mult(a,b),mult(b,mult(c,b))),
inference(paramod,[status(thm)],[c_174,c_694]) ).
cnf(c_658,plain,
$false,
inference(copy,[status(thm)],[c_695]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP697-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.43 % Computer : n010.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Fri Sep 25 15:37:59 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.43 % Process 1125379 was started by sandbox2 on n010,
% 0.15/0.43 % Fri Sep 25 15:37:59 2026
% 0.15/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.44
% 0.15/0.44 % From the command line: assign(max_seconds, 300).
% 2.16/0.73
% 2.16/0.73 % SZS status Unsatisfiable for theBenchmark
% 2.16/0.73
% 2.16/0.73 % Proof 1 at 0.21 (+ 0.07) seconds.
% 2.16/0.73 % Length of proof is 39.
% 2.16/0.73 % Level of proof is 9.
% 2.16/0.73 % Maximum clause weight is 94.000.
% 2.16/0.73 % Given clauses 62.
% 2.16/0.73
% 2.16/0.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------