%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP685-11 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 0.10s 0.42s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of formulae : 75 ( 75 unt; 0 def)
% Number of atoms : 75 ( 74 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 146 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f01,axiom,
! [VAR_0] : ld(VAR_0,mult(VAR_0,VAR_0)) = VAR_0,
file('theBenchmark.p',f01) ).
cnf(c_1,plain,
ld(A,mult(A,A)) = A,
inference(clausify,[status(thm)],[f01]) ).
fof(f02,axiom,
! [VAR_0] : rd(mult(VAR_0,VAR_0),VAR_0) = VAR_0,
file('theBenchmark.p',f02) ).
cnf(c_2,plain,
rd(mult(A,A),A) = A,
inference(clausify,[status(thm)],[f02]) ).
fof(f03,axiom,
! [VAR_0,VAR_1] : mult(VAR_0,ld(VAR_0,VAR_1)) = ld(VAR_0,mult(VAR_0,VAR_1)),
file('theBenchmark.p',f03) ).
cnf(c_3,plain,
mult(A,ld(A,B)) = ld(A,mult(A,B)),
inference(clausify,[status(thm)],[f03]) ).
cnf(c_4,plain,
ld(A,mult(A,B)) = mult(A,ld(A,B)),
inference(copy,[status(thm)],[c_3]) ).
fof(f04,axiom,
! [VAR_0,VAR_1] : mult(rd(VAR_0,VAR_1),VAR_1) = rd(mult(VAR_0,VAR_1),VAR_1),
file('theBenchmark.p',f04) ).
cnf(c_5,plain,
mult(rd(A,B),B) = rd(mult(A,B),B),
inference(clausify,[status(thm)],[f04]) ).
cnf(c_6,plain,
rd(mult(A,B),B) = mult(rd(A,B),B),
inference(copy,[status(thm)],[c_5]) ).
fof(f05,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : ld(ld(VAR_0,VAR_1),mult(ld(VAR_0,VAR_1),mult(VAR_2,VAR_3))) = mult(ld(VAR_0,mult(VAR_0,VAR_2)),VAR_3),
file('theBenchmark.p',f05) ).
cnf(c_7,plain,
ld(ld(A,B),mult(ld(A,B),mult(C,D))) = mult(ld(A,mult(A,C)),D),
inference(clausify,[status(thm)],[f05]) ).
cnf(c_178,plain,
mult(ld(A,B),ld(ld(A,B),mult(C,D))) = mult(ld(A,mult(A,C)),D),
inference(paramod,[status(thm)],[c_4,c_7]) ).
cnf(c_8,plain,
mult(ld(A,B),ld(ld(A,B),mult(C,D))) = mult(mult(A,ld(A,C)),D),
inference(paramod,[status(thm)],[c_4,c_178]) ).
fof(f06,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : rd(mult(mult(VAR_0,VAR_1),rd(VAR_2,VAR_3)),rd(VAR_2,VAR_3)) = mult(VAR_0,rd(mult(VAR_1,VAR_3),VAR_3)),
file('theBenchmark.p',f06) ).
cnf(c_9,plain,
rd(mult(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,rd(mult(B,D),D)),
inference(clausify,[status(thm)],[f06]) ).
cnf(c_179,plain,
mult(rd(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,rd(mult(B,D),D)),
inference(paramod,[status(thm)],[c_6,c_9]) ).
cnf(c_10,plain,
mult(rd(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,mult(rd(B,D),D)),
inference(paramod,[status(thm)],[c_6,c_179]) ).
fof(f07,axiom,
! [VAR_0,VAR_1] : ld(VAR_0,mult(VAR_0,ld(VAR_1,VAR_1))) = rd(mult(rd(VAR_0,VAR_0),VAR_1),VAR_1),
file('theBenchmark.p',f07) ).
cnf(c_11,plain,
ld(A,mult(A,ld(B,B))) = rd(mult(rd(A,A),B),B),
inference(clausify,[status(thm)],[f07]) ).
cnf(c_180,plain,
mult(A,ld(A,ld(B,B))) = rd(mult(rd(A,A),B),B),
inference(paramod,[status(thm)],[c_4,c_11]) ).
cnf(c_181,plain,
mult(A,ld(A,ld(B,B))) = mult(rd(rd(A,A),B),B),
inference(paramod,[status(thm)],[c_6,c_180]) ).
cnf(c_12,plain,
mult(rd(rd(A,A),B),B) = mult(A,ld(A,ld(B,B))),
inference(copy,[status(thm)],[c_181]) ).
fof(goal,axiom,
rd(mult(x6,rd(x7,x8)),rd(x7,x8)) != rd(mult(x6,x8),x8),
file('theBenchmark.p',goal) ).
cnf(c_13,plain,
rd(mult(x6,rd(x7,x8)),rd(x7,x8)) != rd(mult(x6,x8),x8),
inference(clausify,[status(thm)],[goal]) ).
cnf(c_182,plain,
mult(rd(x6,rd(x7,x8)),rd(x7,x8)) != rd(mult(x6,x8),x8),
inference(paramod,[status(thm)],[c_6,c_13]) ).
cnf(c_14,plain,
mult(rd(x6,rd(x7,x8)),rd(x7,x8)) != mult(rd(x6,x8),x8),
inference(paramod,[status(thm)],[c_6,c_182]) ).
cnf(c_15,plain,
mult(A,ld(A,A)) = A,
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_16,plain,
mult(rd(A,A),A) = A,
inference(paramod,[status(thm)],[c_6,c_2]) ).
cnf(c_183,plain,
mult(mult(A,ld(A,B)),ld(ld(A,mult(A,B)),mult(C,D))) = mult(mult(A,ld(A,C)),D),
inference(paramod,[status(thm)],[c_4,c_8]) ).
cnf(c_18,plain,
mult(mult(A,ld(A,B)),ld(mult(A,ld(A,B)),mult(C,D))) = mult(mult(A,ld(A,C)),D),
inference(paramod,[status(thm)],[c_4,c_183]) ).
cnf(c_184,plain,
ld(A,A) = mult(A,ld(A,ld(A,A))),
inference(paramod,[status(thm)],[c_15,c_4]) ).
cnf(c_33,plain,
mult(A,ld(A,ld(A,A))) = ld(A,A),
inference(copy,[status(thm)],[c_184]) ).
cnf(c_185,plain,
rd(A,ld(A,A)) = mult(rd(A,ld(A,A)),ld(A,A)),
inference(paramod,[status(thm)],[c_15,c_6]) ).
cnf(c_34,plain,
mult(rd(A,ld(A,A)),ld(A,A)) = rd(A,ld(A,A)),
inference(copy,[status(thm)],[c_185]) ).
cnf(c_36,plain,
mult(rd(A,rd(B,C)),rd(B,C)) = mult(A,mult(rd(ld(A,A),C),C)),
inference(paramod,[status(thm)],[c_15,c_10]) ).
cnf(c_186,plain,
rd(A,A) = mult(rd(rd(A,A),A),A),
inference(paramod,[status(thm)],[c_16,c_6]) ).
cnf(c_187,plain,
rd(A,A) = mult(A,ld(A,ld(A,A))),
inference(paramod,[status(thm)],[c_12,c_186]) ).
cnf(c_38,plain,
rd(A,A) = ld(A,A),
inference(paramod,[status(thm)],[c_33,c_187]) ).
cnf(c_188,plain,
rd(mult(A,A),A) = A,
inference(paramod,[status(thm)],[c_16,c_6]) ).
cnf(c_189,plain,
mult(rd(A,A),A) = A,
inference(paramod,[status(thm)],[c_6,c_188]) ).
cnf(c_39,plain,
mult(ld(A,A),A) = A,
inference(paramod,[status(thm)],[c_38,c_189]) ).
cnf(c_48,plain,
mult(rd(ld(A,A),B),B) = mult(A,ld(A,ld(B,B))),
inference(paramod,[status(thm)],[c_38,c_12]) ).
cnf(c_49,plain,
mult(rd(A,rd(B,C)),rd(B,C)) = mult(A,mult(A,ld(A,ld(C,C)))),
inference(paramod,[status(thm)],[c_48,c_36]) ).
cnf(c_190,plain,
mult(rd(mult(A,B),ld(C,C)),rd(C,C)) = mult(A,mult(rd(B,C),C)),
inference(paramod,[status(thm)],[c_38,c_10]) ).
cnf(c_53,plain,
mult(rd(mult(A,B),ld(C,C)),ld(C,C)) = mult(A,mult(rd(B,C),C)),
inference(paramod,[status(thm)],[c_38,c_190]) ).
cnf(c_191,plain,
mult(rd(A,ld(B,B)),ld(B,B)) = mult(A,mult(rd(ld(A,A),B),B)),
inference(paramod,[status(thm)],[c_15,c_53]) ).
cnf(c_70,plain,
mult(rd(A,ld(B,B)),ld(B,B)) = mult(A,mult(A,ld(A,ld(B,B)))),
inference(paramod,[status(thm)],[c_48,c_191]) ).
cnf(c_192,plain,
mult(A,ld(mult(A,ld(A,A)),mult(B,C))) = mult(mult(A,ld(A,B)),C),
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_193,plain,
mult(A,ld(A,mult(B,C))) = mult(mult(A,ld(A,B)),C),
inference(paramod,[status(thm)],[c_15,c_192]) ).
cnf(c_81,plain,
mult(mult(A,ld(A,B)),C) = mult(A,ld(A,mult(B,C))),
inference(copy,[status(thm)],[c_193]) ).
cnf(c_194,plain,
mult(mult(A,ld(A,B)),ld(mult(A,ld(A,B)),C)) = mult(mult(A,ld(A,C)),ld(C,C)),
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_195,plain,
mult(A,ld(A,mult(B,ld(mult(A,ld(A,B)),C)))) = mult(mult(A,ld(A,C)),ld(C,C)),
inference(paramod,[status(thm)],[c_81,c_194]) ).
cnf(c_196,plain,
mult(A,ld(A,mult(B,ld(mult(A,ld(A,B)),C)))) = mult(A,ld(A,mult(C,ld(C,C)))),
inference(paramod,[status(thm)],[c_81,c_195]) ).
cnf(c_82,plain,
mult(A,ld(A,mult(B,ld(mult(A,ld(A,B)),C)))) = mult(A,ld(A,C)),
inference(paramod,[status(thm)],[c_15,c_196]) ).
cnf(c_197,plain,
mult(mult(A,ld(A,B)),ld(mult(A,ld(A,B)),mult(A,C))) = mult(A,C),
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_198,plain,
mult(A,ld(A,mult(B,ld(mult(A,ld(A,B)),mult(A,C))))) = mult(A,C),
inference(paramod,[status(thm)],[c_81,c_197]) ).
cnf(c_199,plain,
mult(A,ld(A,mult(A,C))) = mult(A,C),
inference(paramod,[status(thm)],[c_82,c_198]) ).
cnf(c_83,plain,
mult(A,mult(A,ld(A,B))) = mult(A,B),
inference(paramod,[status(thm)],[c_4,c_199]) ).
cnf(c_104,plain,
mult(rd(A,ld(B,B)),ld(B,B)) = mult(A,ld(B,B)),
inference(paramod,[status(thm)],[c_83,c_70]) ).
cnf(c_105,plain,
mult(rd(A,rd(B,C)),rd(B,C)) = mult(A,ld(C,C)),
inference(paramod,[status(thm)],[c_83,c_49]) ).
cnf(c_200,plain,
mult(A,ld(A,A)) = rd(A,ld(A,A)),
inference(paramod,[status(thm)],[c_104,c_34]) ).
cnf(c_201,plain,
A = rd(A,ld(A,A)),
inference(paramod,[status(thm)],[c_15,c_200]) ).
cnf(c_115,plain,
rd(A,ld(A,A)) = A,
inference(copy,[status(thm)],[c_201]) ).
cnf(c_202,plain,
mult(x6,ld(x8,x8)) != mult(rd(x6,x8),x8),
inference(paramod,[status(thm)],[c_105,c_14]) ).
cnf(c_118,plain,
mult(rd(x6,x8),x8) != mult(x6,ld(x8,x8)),
inference(copy,[status(thm)],[c_202]) ).
cnf(c_203,plain,
mult(ld(ld(A,A),ld(A,A)),ld(A,A)) = mult(ld(A,A),ld(A,A)),
inference(paramod,[status(thm)],[c_38,c_104]) ).
cnf(c_204,plain,
ld(A,A) = mult(ld(A,A),ld(A,A)),
inference(paramod,[status(thm)],[c_39,c_203]) ).
cnf(c_123,plain,
mult(ld(A,A),ld(A,A)) = ld(A,A),
inference(copy,[status(thm)],[c_204]) ).
cnf(c_205,plain,
ld(ld(A,A),ld(A,A)) = mult(ld(A,A),ld(ld(A,A),ld(A,A))),
inference(paramod,[status(thm)],[c_123,c_4]) ).
cnf(c_127,plain,
ld(ld(A,A),ld(A,A)) = ld(A,A),
inference(paramod,[status(thm)],[c_15,c_205]) ).
cnf(c_206,plain,
mult(rd(A,B),rd(B,ld(B,B))) = mult(A,ld(ld(B,B),ld(B,B))),
inference(paramod,[status(thm)],[c_115,c_105]) ).
cnf(c_207,plain,
mult(rd(A,B),B) = mult(A,ld(ld(B,B),ld(B,B))),
inference(paramod,[status(thm)],[c_115,c_206]) ).
cnf(c_176,plain,
mult(rd(A,B),B) = mult(A,ld(B,B)),
inference(paramod,[status(thm)],[c_127,c_207]) ).
cnf(c_177,plain,
$false,
inference(resolve,[status(thm)],[c_176,c_118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP685-11 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 15:40:09 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2919104 was started by sandbox2 on n026,
% 0.10/0.37 % Fri Sep 25 15:40:09 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.42
% 0.10/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.42
% 0.10/0.42 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.10/0.42 % Length of proof is 37.
% 0.10/0.42 % Level of proof is 11.
% 0.10/0.42 % Maximum clause weight is 59.000.
% 0.10/0.42 % Given clauses 30.
% 0.10/0.42
% 0.10/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------