%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP686-1 : 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 : n009.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 07:31:12 AM UTC 2026
% Result : Unsatisfiable 2.36s 0.78s
% Output : CNFRefutation 2.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 8
% Syntax : Number of formulae : 101 ( 101 unt; 0 def)
% Number of atoms : 101 ( 100 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 213 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(c01,axiom,
! [VAR_0,VAR_1] : mult(VAR_0,ld(VAR_0,VAR_1)) = VAR_1,
file('theBenchmark.p',c01) ).
cnf(c_1,plain,
mult(A,ld(A,B)) = B,
inference(clausify,[status(thm)],[c01]) ).
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(c04,axiom,
! [VAR_0,VAR_1] : rd(mult(VAR_0,VAR_1),VAR_1) = VAR_0,
file('theBenchmark.p',c04) ).
cnf(c_4,plain,
rd(mult(A,B),B) = A,
inference(clausify,[status(thm)],[c04]) ).
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,VAR_2] : mult(VAR_0,mult(VAR_1,mult(VAR_1,VAR_2))) = mult(mult(VAR_0,mult(VAR_1,VAR_1)),VAR_2),
file('theBenchmark.p',c07) ).
cnf(c_7,plain,
mult(A,mult(B,mult(B,C))) = mult(mult(A,mult(B,B)),C),
inference(clausify,[status(thm)],[c07]) ).
cnf(c_8,plain,
mult(mult(A,mult(B,B)),C) = mult(A,mult(B,mult(B,C))),
inference(copy,[status(thm)],[c_7]) ).
fof(goals,axiom,
mult(mult(a,a),mult(b,c)) != mult(mult(a,mult(a,b)),c),
file('theBenchmark.p',goals) ).
cnf(c_9,plain,
mult(mult(a,a),mult(b,c)) != mult(mult(a,mult(a,b)),c),
inference(clausify,[status(thm)],[goals]) ).
cnf(c_10,plain,
mult(mult(a,mult(a,b)),c) != mult(mult(a,a),mult(b,c)),
inference(copy,[status(thm)],[c_9]) ).
cnf(c_11,plain,
ld(rd(A,B),A) = B,
inference(paramod,[status(thm)],[c_3,c_2]) ).
cnf(c_12,plain,
rd(A,ld(B,A)) = B,
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_13,plain,
ld(A,A) = unit,
inference(paramod,[status(thm)],[c_5,c_2]) ).
cnf(c_17,plain,
mult(A,mult(B,mult(B,ld(mult(A,mult(B,B)),C)))) = C,
inference(paramod,[status(thm)],[c_8,c_1]) ).
cnf(c_1123,plain,
mult(A,B) = mult(rd(A,mult(C,C)),mult(C,mult(C,B))),
inference(paramod,[status(thm)],[c_3,c_8]) ).
cnf(c_19,plain,
mult(rd(A,mult(B,B)),mult(B,mult(B,C))) = mult(A,C),
inference(copy,[status(thm)],[c_1123]) ).
cnf(c_20,plain,
rd(mult(A,mult(B,mult(B,C))),C) = mult(A,mult(B,B)),
inference(paramod,[status(thm)],[c_8,c_4]) ).
cnf(c_1124,plain,
mult(mult(A,A),B) = mult(unit,mult(A,mult(A,B))),
inference(paramod,[status(thm)],[c_6,c_8]) ).
cnf(c_21,plain,
mult(mult(A,A),B) = mult(A,mult(A,B)),
inference(paramod,[status(thm)],[c_6,c_1124]) ).
cnf(c_23,plain,
mult(mult(a,mult(a,b)),c) != mult(a,mult(a,mult(b,c))),
inference(paramod,[status(thm)],[c_21,c_10]) ).
cnf(c_1125,plain,
ld(A,B) = mult(C,mult(C,ld(mult(A,mult(C,C)),B))),
inference(paramod,[status(thm)],[c_17,c_2]) ).
cnf(c_28,plain,
mult(A,mult(A,ld(mult(B,mult(A,A)),C))) = ld(B,C),
inference(copy,[status(thm)],[c_1125]) ).
cnf(c_72,plain,
mult(rd(A,mult(B,B)),mult(B,C)) = mult(A,ld(B,C)),
inference(paramod,[status(thm)],[c_1,c_19]) ).
cnf(c_89,plain,
mult(rd(A,mult(B,B)),C) = mult(A,ld(B,ld(B,C))),
inference(paramod,[status(thm)],[c_1,c_72]) ).
cnf(c_90,plain,
rd(mult(A,ld(B,C)),mult(B,C)) = rd(A,mult(B,B)),
inference(paramod,[status(thm)],[c_72,c_4]) ).
cnf(c_103,plain,
rd(A,mult(B,A)) = rd(B,mult(B,B)),
inference(paramod,[status(thm)],[c_1,c_90]) ).
cnf(c_1126,plain,
rd(A,B) = rd(rd(B,A),mult(rd(B,A),rd(B,A))),
inference(paramod,[status(thm)],[c_3,c_103]) ).
cnf(c_117,plain,
rd(rd(A,B),mult(rd(A,B),rd(A,B))) = rd(B,A),
inference(copy,[status(thm)],[c_1126]) ).
cnf(c_1127,plain,
rd(unit,A) = rd(A,mult(A,A)),
inference(paramod,[status(thm)],[c_5,c_103]) ).
cnf(c_118,plain,
rd(A,mult(A,A)) = rd(unit,A),
inference(copy,[status(thm)],[c_1127]) ).
cnf(c_1128,plain,
ld(rd(A,mult(A,A)),B) = mult(A,B),
inference(paramod,[status(thm)],[c_103,c_11]) ).
cnf(c_120,plain,
ld(rd(unit,A),B) = mult(A,B),
inference(paramod,[status(thm)],[c_118,c_1128]) ).
cnf(c_1129,plain,
rd(mult(A,ld(A,B)),mult(A,B)) = rd(A,mult(A,A)),
inference(paramod,[status(thm)],[c_103,c_90]) ).
cnf(c_1130,plain,
rd(B,mult(A,B)) = rd(A,mult(A,A)),
inference(paramod,[status(thm)],[c_1,c_1129]) ).
cnf(c_133,plain,
rd(A,mult(B,A)) = rd(unit,B),
inference(paramod,[status(thm)],[c_118,c_1130]) ).
cnf(c_134,plain,
rd(unit,rd(A,B)) = rd(B,A),
inference(paramod,[status(thm)],[c_118,c_117]) ).
cnf(c_160,plain,
mult(A,rd(unit,A)) = unit,
inference(paramod,[status(thm)],[c_120,c_13]) ).
cnf(c_1131,plain,
ld(A,B) = mult(ld(A,unit),B),
inference(paramod,[status(thm)],[c_12,c_120]) ).
cnf(c_161,plain,
mult(ld(A,unit),B) = ld(A,B),
inference(copy,[status(thm)],[c_1131]) ).
cnf(c_1132,plain,
ld(A,unit) = rd(unit,A),
inference(paramod,[status(thm)],[c_160,c_2]) ).
cnf(c_164,plain,
rd(unit,A) = ld(A,unit),
inference(copy,[status(thm)],[c_1132]) ).
cnf(c_1133,plain,
rd(mult(A,mult(B,unit)),rd(unit,B)) = mult(A,mult(B,B)),
inference(paramod,[status(thm)],[c_160,c_20]) ).
cnf(c_1134,plain,
rd(mult(A,B),rd(unit,B)) = mult(A,mult(B,B)),
inference(paramod,[status(thm)],[c_5,c_1133]) ).
cnf(c_166,plain,
rd(mult(A,B),ld(B,unit)) = mult(A,mult(B,B)),
inference(paramod,[status(thm)],[c_164,c_1134]) ).
cnf(c_174,plain,
ld(rd(A,B),unit) = rd(B,A),
inference(paramod,[status(thm)],[c_164,c_134]) ).
cnf(c_175,plain,
rd(A,mult(B,A)) = ld(B,unit),
inference(paramod,[status(thm)],[c_164,c_133]) ).
cnf(c_177,plain,
ld(ld(A,unit),B) = mult(A,B),
inference(paramod,[status(thm)],[c_164,c_120]) ).
cnf(c_1135,plain,
mult(ld(A,mult(B,B)),C) = mult(ld(A,unit),mult(B,mult(B,C))),
inference(paramod,[status(thm)],[c_161,c_8]) ).
cnf(c_1136,plain,
mult(ld(A,mult(B,B)),C) = ld(A,mult(B,mult(B,C))),
inference(paramod,[status(thm)],[c_161,c_1135]) ).
cnf(c_183,plain,
ld(A,mult(B,mult(B,C))) = mult(ld(A,mult(B,B)),C),
inference(copy,[status(thm)],[c_1136]) ).
cnf(c_1137,plain,
ld(rd(A,mult(B,B)),unit) = rd(mult(B,C),mult(A,ld(B,C))),
inference(paramod,[status(thm)],[c_90,c_174]) ).
cnf(c_1138,plain,
rd(mult(B,B),A) = rd(mult(B,C),mult(A,ld(B,C))),
inference(paramod,[status(thm)],[c_174,c_1137]) ).
cnf(c_198,plain,
rd(mult(A,B),mult(C,ld(A,B))) = rd(mult(A,A),C),
inference(copy,[status(thm)],[c_1138]) ).
cnf(c_1139,plain,
mult(rd(A,B),C) = ld(rd(B,A),C),
inference(paramod,[status(thm)],[c_174,c_161]) ).
cnf(c_199,plain,
ld(rd(A,B),C) = mult(rd(B,A),C),
inference(copy,[status(thm)],[c_1139]) ).
cnf(c_1140,plain,
rd(ld(A,B),ld(B,unit)) = mult(ld(A,unit),mult(B,B)),
inference(paramod,[status(thm)],[c_161,c_166]) ).
cnf(c_241,plain,
rd(ld(A,B),ld(B,unit)) = ld(A,mult(B,B)),
inference(paramod,[status(thm)],[c_161,c_1140]) ).
cnf(c_247,plain,
mult(ld(A,mult(B,B)),ld(B,unit)) = ld(A,B),
inference(paramod,[status(thm)],[c_241,c_3]) ).
cnf(c_1141,plain,
mult(A,mult(A,ld(B,C))) = ld(rd(B,mult(A,A)),C),
inference(paramod,[status(thm)],[c_3,c_28]) ).
cnf(c_1142,plain,
mult(A,mult(A,ld(B,C))) = mult(rd(mult(A,A),B),C),
inference(paramod,[status(thm)],[c_199,c_1141]) ).
cnf(c_260,plain,
mult(rd(mult(A,A),B),C) = mult(A,mult(A,ld(B,C))),
inference(copy,[status(thm)],[c_1142]) ).
cnf(c_295,plain,
rd(ld(A,unit),ld(B,A)) = ld(ld(B,mult(A,A)),unit),
inference(paramod,[status(thm)],[c_247,c_175]) ).
cnf(c_317,plain,
rd(A,mult(B,ld(A,unit))) = rd(mult(A,A),B),
inference(paramod,[status(thm)],[c_5,c_198]) ).
cnf(c_1143,plain,
rd(A,ld(B,ld(A,unit))) = rd(mult(A,A),ld(B,unit)),
inference(paramod,[status(thm)],[c_161,c_317]) ).
cnf(c_336,plain,
rd(mult(A,A),ld(B,unit)) = rd(A,ld(B,ld(A,unit))),
inference(copy,[status(thm)],[c_1143]) ).
cnf(c_1144,plain,
ld(A,mult(B,C)) = mult(ld(A,mult(B,B)),ld(B,C)),
inference(paramod,[status(thm)],[c_1,c_183]) ).
cnf(c_515,plain,
mult(ld(A,mult(B,B)),ld(B,C)) = ld(A,mult(B,C)),
inference(copy,[status(thm)],[c_1144]) ).
cnf(c_533,plain,
rd(ld(A,mult(B,C)),ld(B,C)) = ld(A,mult(B,B)),
inference(paramod,[status(thm)],[c_515,c_4]) ).
cnf(c_1145,plain,
rd(unit,ld(A,B)) = ld(mult(A,B),mult(A,A)),
inference(paramod,[status(thm)],[c_13,c_533]) ).
cnf(c_1146,plain,
ld(ld(A,B),unit) = ld(mult(A,B),mult(A,A)),
inference(paramod,[status(thm)],[c_164,c_1145]) ).
cnf(c_550,plain,
ld(mult(A,B),mult(A,A)) = ld(ld(A,B),unit),
inference(copy,[status(thm)],[c_1146]) ).
cnf(c_1147,plain,
ld(A,mult(rd(A,B),rd(A,B))) = ld(ld(rd(A,B),B),unit),
inference(paramod,[status(thm)],[c_3,c_550]) ).
cnf(c_566,plain,
ld(A,mult(rd(A,B),rd(A,B))) = ld(mult(rd(B,A),B),unit),
inference(paramod,[status(thm)],[c_199,c_1147]) ).
cnf(c_1148,plain,
mult(ld(mult(rd(A,B),A),unit),ld(rd(B,A),C)) = ld(B,mult(rd(B,A),C)),
inference(paramod,[status(thm)],[c_566,c_515]) ).
cnf(c_1149,plain,
mult(ld(mult(rd(A,B),A),unit),mult(rd(A,B),C)) = ld(B,mult(rd(B,A),C)),
inference(paramod,[status(thm)],[c_199,c_1148]) ).
cnf(c_631,plain,
ld(mult(rd(A,B),A),mult(rd(A,B),C)) = ld(B,mult(rd(B,A),C)),
inference(paramod,[status(thm)],[c_161,c_1149]) ).
cnf(c_695,plain,
ld(mult(rd(A,B),A),A) = ld(B,mult(rd(B,A),B)),
inference(paramod,[status(thm)],[c_3,c_631]) ).
cnf(c_1150,plain,
rd(ld(mult(rd(mult(A,A),B),mult(A,A)),A),ld(A,unit)) = ld(B,mult(rd(B,mult(A,A)),B)),
inference(paramod,[status(thm)],[c_695,c_241]) ).
cnf(c_1151,plain,
rd(ld(mult(A,mult(A,ld(B,mult(A,A)))),A),ld(A,unit)) = ld(B,mult(rd(B,mult(A,A)),B)),
inference(paramod,[status(thm)],[c_260,c_1150]) ).
cnf(c_1152,plain,
ld(mult(A,mult(A,ld(B,mult(A,A)))),mult(A,A)) = ld(B,mult(rd(B,mult(A,A)),B)),
inference(paramod,[status(thm)],[c_241,c_1151]) ).
cnf(c_1153,plain,
ld(ld(A,mult(A,ld(B,mult(A,A)))),unit) = ld(B,mult(rd(B,mult(A,A)),B)),
inference(paramod,[status(thm)],[c_550,c_1152]) ).
cnf(c_1154,plain,
ld(ld(B,mult(A,A)),unit) = ld(B,mult(rd(B,mult(A,A)),B)),
inference(paramod,[status(thm)],[c_2,c_1153]) ).
cnf(c_1155,plain,
ld(ld(B,mult(A,A)),unit) = ld(B,mult(B,ld(A,ld(A,B)))),
inference(paramod,[status(thm)],[c_89,c_1154]) ).
cnf(c_746,plain,
ld(ld(A,mult(B,B)),unit) = ld(B,ld(B,A)),
inference(paramod,[status(thm)],[c_2,c_1155]) ).
cnf(c_789,plain,
rd(ld(A,unit),ld(B,A)) = ld(A,ld(A,B)),
inference(paramod,[status(thm)],[c_746,c_295]) ).
cnf(c_1156,plain,
rd(mult(A,unit),ld(B,ld(A,unit))) = ld(ld(A,unit),ld(ld(A,unit),B)),
inference(paramod,[status(thm)],[c_177,c_789]) ).
cnf(c_1157,plain,
rd(A,ld(B,ld(A,unit))) = ld(ld(A,unit),ld(ld(A,unit),B)),
inference(paramod,[status(thm)],[c_5,c_1156]) ).
cnf(c_1158,plain,
rd(A,ld(B,ld(A,unit))) = ld(ld(A,unit),mult(A,B)),
inference(paramod,[status(thm)],[c_177,c_1157]) ).
cnf(c_809,plain,
rd(A,ld(B,ld(A,unit))) = mult(A,mult(A,B)),
inference(paramod,[status(thm)],[c_177,c_1158]) ).
cnf(c_831,plain,
rd(mult(A,A),ld(B,unit)) = mult(A,mult(A,B)),
inference(paramod,[status(thm)],[c_809,c_336]) ).
cnf(c_1159,plain,
mult(rd(mult(A,A),ld(B,unit)),C) = mult(A,mult(A,mult(B,C))),
inference(paramod,[status(thm)],[c_177,c_260]) ).
cnf(c_1121,plain,
mult(mult(A,mult(A,B)),C) = mult(A,mult(A,mult(B,C))),
inference(paramod,[status(thm)],[c_831,c_1159]) ).
cnf(c_1122,plain,
$false,
inference(resolve,[status(thm)],[c_1121,c_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP686-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n009.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Fri Sep 25 15:37:28 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.39 % Process 1955158 was started by sandbox2 on n009,
% 0.12/0.39 % Fri Sep 25 15:37:28 2026
% 0.12/0.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.39
% 0.12/0.39 % From the command line: assign(max_seconds, 300).
% 2.36/0.78
% 2.36/0.78 % SZS status Unsatisfiable for theBenchmark
% 2.36/0.78
% 2.36/0.78 % Proof 1 at 0.27 (+ 0.09) seconds.
% 2.36/0.78 % Length of proof is 56.
% 2.36/0.78 % Level of proof is 21.
% 2.36/0.78 % Maximum clause weight is 65.000.
% 2.36/0.78 % Given clauses 91.
% 2.36/0.78
% 2.36/0.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------