%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP750-1 : 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 : n001.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 07:31:22 AM UTC 2026
% Result : Unsatisfiable 13.87s 12.43s
% Output : CNFRefutation 13.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 7
% Syntax : Number of formulae : 59 ( 59 unt; 0 def)
% Number of atoms : 59 ( 58 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 6 ( 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 : 155 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f01,axiom,
! [VAR_0,VAR_1] : mult(VAR_0,ld(VAR_0,VAR_1)) = VAR_1,
file('theBenchmark.p',f01) ).
cnf(c_1,plain,
mult(A,ld(A,B)) = B,
inference(clausify,[status(thm)],[f01]) ).
fof(f02,axiom,
! [VAR_0,VAR_1] : ld(VAR_0,mult(VAR_0,VAR_1)) = VAR_1,
file('theBenchmark.p',f02) ).
cnf(c_2,plain,
ld(A,mult(A,B)) = B,
inference(clausify,[status(thm)],[f02]) ).
fof(f03,axiom,
! [VAR_0,VAR_1] : mult(rd(VAR_0,VAR_1),VAR_1) = VAR_0,
file('theBenchmark.p',f03) ).
cnf(c_3,plain,
mult(rd(A,B),B) = A,
inference(clausify,[status(thm)],[f03]) ).
fof(f04,axiom,
! [VAR_0,VAR_1] : rd(mult(VAR_0,VAR_1),VAR_1) = VAR_0,
file('theBenchmark.p',f04) ).
cnf(c_4,plain,
rd(mult(A,B),B) = A,
inference(clausify,[status(thm)],[f04]) ).
fof(f05,axiom,
! [VAR_0,VAR_1,VAR_2] : mult(mult(VAR_0,mult(VAR_0,VAR_0)),mult(VAR_1,VAR_2)) = mult(mult(VAR_0,VAR_1),mult(mult(VAR_0,VAR_0),VAR_2)),
file('theBenchmark.p',f05) ).
cnf(c_5,plain,
mult(mult(A,mult(A,A)),mult(B,C)) = mult(mult(A,B),mult(mult(A,A),C)),
inference(clausify,[status(thm)],[f05]) ).
fof(f06,axiom,
! [VAR_0,VAR_1,VAR_2] : mult(mult(VAR_0,VAR_1),mult(VAR_2,VAR_2)) = mult(mult(VAR_0,VAR_2),mult(VAR_1,VAR_2)),
file('theBenchmark.p',f06) ).
cnf(c_6,plain,
mult(mult(A,B),mult(C,C)) = mult(mult(A,C),mult(B,C)),
inference(clausify,[status(thm)],[f06]) ).
fof(goals,axiom,
mult(mult(a,a),mult(b,c)) != mult(mult(a,b),mult(a,c)),
file('theBenchmark.p',goals) ).
cnf(c_7,plain,
mult(mult(a,a),mult(b,c)) != mult(mult(a,b),mult(a,c)),
inference(clausify,[status(thm)],[goals]) ).
cnf(c_8,plain,
mult(mult(a,b),mult(a,c)) != mult(mult(a,a),mult(b,c)),
inference(copy,[status(thm)],[c_7]) ).
cnf(c_9,plain,
ld(rd(A,B),A) = B,
inference(paramod,[status(thm)],[c_3,c_2]) ).
cnf(c_10,plain,
rd(A,ld(B,A)) = B,
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_13,plain,
mult(mult(A,mult(A,A)),mult(B,ld(mult(A,A),C))) = mult(mult(A,B),C),
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_28,plain,
ld(mult(A,B),mult(mult(A,C),mult(B,C))) = mult(C,C),
inference(paramod,[status(thm)],[c_6,c_2]) ).
cnf(c_29,plain,
ld(mult(A,B),mult(mult(A,C),mult(B,B))) = mult(C,B),
inference(paramod,[status(thm)],[c_6,c_2]) ).
cnf(c_31,plain,
mult(mult(rd(A,B),C),mult(B,B)) = mult(A,mult(C,B)),
inference(paramod,[status(thm)],[c_3,c_6]) ).
cnf(c_61,plain,
ld(mult(rd(A,B),C),mult(A,mult(C,B))) = mult(B,B),
inference(paramod,[status(thm)],[c_3,c_28]) ).
cnf(c_77,plain,
ld(mult(rd(A,ld(B,C)),B),mult(A,C)) = mult(ld(B,C),ld(B,C)),
inference(paramod,[status(thm)],[c_1,c_61]) ).
cnf(c_78,plain,
ld(mult(rd(A,B),rd(C,B)),mult(A,C)) = mult(B,B),
inference(paramod,[status(thm)],[c_3,c_61]) ).
cnf(c_93,plain,
rd(mult(A,B),mult(C,C)) = mult(rd(A,C),rd(B,C)),
inference(paramod,[status(thm)],[c_78,c_10]) ).
cnf(c_5039,plain,
rd(A,mult(B,B)) = mult(rd(rd(A,C),B),rd(C,B)),
inference(paramod,[status(thm)],[c_3,c_93]) ).
cnf(c_96,plain,
mult(rd(rd(A,B),C),rd(B,C)) = rd(A,mult(C,C)),
inference(copy,[status(thm)],[c_5039]) ).
cnf(c_195,plain,
mult(rd(rd(A,mult(B,C)),C),B) = rd(A,mult(C,C)),
inference(paramod,[status(thm)],[c_4,c_96]) ).
cnf(c_221,plain,
ld(mult(A,B),mult(C,mult(B,B))) = mult(ld(A,C),B),
inference(paramod,[status(thm)],[c_1,c_29]) ).
cnf(c_252,plain,
ld(A,mult(B,mult(C,C))) = mult(ld(rd(A,C),B),C),
inference(paramod,[status(thm)],[c_3,c_221]) ).
cnf(c_258,plain,
rd(mult(A,mult(B,B)),mult(ld(C,A),B)) = mult(C,B),
inference(paramod,[status(thm)],[c_221,c_10]) ).
cnf(c_268,plain,
ld(A,mult(mult(B,C),mult(D,C))) = mult(ld(rd(A,C),mult(B,D)),C),
inference(paramod,[status(thm)],[c_6,c_252]) ).
cnf(c_287,plain,
rd(mult(A,mult(B,B)),mult(C,B)) = mult(rd(A,C),B),
inference(paramod,[status(thm)],[c_9,c_258]) ).
cnf(c_298,plain,
rd(mult(A,mult(B,B)),C) = mult(rd(A,rd(C,B)),B),
inference(paramod,[status(thm)],[c_3,c_287]) ).
cnf(c_350,plain,
ld(mult(A,mult(A,A)),mult(mult(A,B),C)) = mult(B,ld(mult(A,A),C)),
inference(paramod,[status(thm)],[c_13,c_2]) ).
cnf(c_5040,plain,
ld(mult(A,mult(A,A)),mult(mult(A,B),mult(C,B))) = mult(C,ld(mult(A,A),mult(B,B))),
inference(paramod,[status(thm)],[c_6,c_350]) ).
cnf(c_5041,plain,
mult(ld(rd(mult(A,mult(A,A)),B),mult(A,C)),B) = mult(C,ld(mult(A,A),mult(B,B))),
inference(paramod,[status(thm)],[c_268,c_5040]) ).
cnf(c_1383,plain,
mult(ld(mult(rd(A,rd(B,A)),A),mult(A,C)),B) = mult(C,ld(mult(A,A),mult(B,B))),
inference(paramod,[status(thm)],[c_298,c_5041]) ).
cnf(c_5042,plain,
ld(mult(A,mult(A,A)),mult(mult(A,B),mult(C,C))) = mult(C,ld(mult(A,A),mult(B,C))),
inference(paramod,[status(thm)],[c_6,c_350]) ).
cnf(c_5043,plain,
mult(ld(rd(mult(A,mult(A,A)),C),mult(A,B)),C) = mult(C,ld(mult(A,A),mult(B,C))),
inference(paramod,[status(thm)],[c_252,c_5042]) ).
cnf(c_5044,plain,
mult(ld(mult(rd(A,rd(C,A)),A),mult(A,B)),C) = mult(C,ld(mult(A,A),mult(B,C))),
inference(paramod,[status(thm)],[c_298,c_5043]) ).
cnf(c_1385,plain,
mult(A,ld(mult(B,B),mult(C,C))) = mult(C,ld(mult(B,B),mult(A,C))),
inference(paramod,[status(thm)],[c_1383,c_5044]) ).
cnf(c_1397,plain,
ld(A,mult(B,ld(mult(C,C),mult(A,A)))) = ld(mult(C,C),mult(B,A)),
inference(paramod,[status(thm)],[c_1385,c_2]) ).
cnf(c_2262,plain,
ld(mult(A,A),mult(B,B)) = mult(ld(A,B),ld(A,B)),
inference(paramod,[status(thm)],[c_10,c_77]) ).
cnf(c_5045,plain,
ld(A,mult(B,mult(ld(C,A),ld(C,A)))) = ld(mult(C,C),mult(B,A)),
inference(paramod,[status(thm)],[c_2262,c_1397]) ).
cnf(c_5046,plain,
mult(ld(rd(A,ld(C,A)),B),ld(C,A)) = ld(mult(C,C),mult(B,A)),
inference(paramod,[status(thm)],[c_252,c_5045]) ).
cnf(c_5047,plain,
mult(ld(C,B),ld(C,A)) = ld(mult(C,C),mult(B,A)),
inference(paramod,[status(thm)],[c_10,c_5046]) ).
cnf(c_2520,plain,
ld(mult(A,A),mult(B,C)) = mult(ld(A,B),ld(A,C)),
inference(copy,[status(thm)],[c_5047]) ).
cnf(c_2646,plain,
rd(mult(A,B),mult(ld(C,A),ld(C,B))) = mult(C,C),
inference(paramod,[status(thm)],[c_2520,c_10]) ).
cnf(c_2780,plain,
rd(mult(A,mult(B,C)),mult(ld(B,A),C)) = mult(B,B),
inference(paramod,[status(thm)],[c_2,c_2646]) ).
cnf(c_5048,plain,
mult(rd(mult(A,A),B),ld(A,C)) = rd(mult(C,mult(A,B)),mult(B,B)),
inference(paramod,[status(thm)],[c_2780,c_195]) ).
cnf(c_5049,plain,
mult(rd(mult(A,A),B),ld(A,C)) = mult(rd(C,B),rd(mult(A,B),B)),
inference(paramod,[status(thm)],[c_93,c_5048]) ).
cnf(c_3417,plain,
mult(rd(mult(A,A),B),ld(A,C)) = mult(rd(C,B),A),
inference(paramod,[status(thm)],[c_4,c_5049]) ).
cnf(c_5050,plain,
mult(rd(mult(A,A),B),C) = mult(rd(mult(A,C),B),A),
inference(paramod,[status(thm)],[c_2,c_3417]) ).
cnf(c_3921,plain,
mult(rd(mult(A,B),C),A) = mult(rd(mult(A,A),C),B),
inference(copy,[status(thm)],[c_5050]) ).
cnf(c_5051,plain,
mult(mult(rd(mult(A,A),B),C),mult(B,B)) = mult(mult(A,C),mult(A,B)),
inference(paramod,[status(thm)],[c_3921,c_31]) ).
cnf(c_5052,plain,
mult(mult(A,A),mult(C,B)) = mult(mult(A,C),mult(A,B)),
inference(paramod,[status(thm)],[c_31,c_5051]) ).
cnf(c_5037,plain,
mult(mult(A,B),mult(A,C)) = mult(mult(A,A),mult(B,C)),
inference(copy,[status(thm)],[c_5052]) ).
cnf(c_5038,plain,
$false,
inference(resolve,[status(thm)],[c_5037,c_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP750-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/10.40 % Computer : n001.cluster.edu
% 0.11/10.40 % Model : x86_64 x86_64
% 0.11/10.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.40 % Memory : 8046.5625MB
% 0.11/10.40 % OS : Linux 6.8.0-71-generic
% 0.11/10.40 % CPULimit : 300
% 0.11/10.40 % WCLimit : 300
% 0.11/10.40 % DateTime : Fri Sep 25 15:49:20 UTC 2026
% 0.11/10.40 % CPUTime :
% 0.11/10.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/10.41 % Process 3736307 was started by sandbox2 on n001,
% 0.11/10.41 % Fri Sep 25 15:49:20 2026
% 0.11/10.41 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/10.41
% 0.11/10.41 % From the command line: assign(max_seconds, 300).
% 13.87/12.43
% 13.87/12.43 % SZS status Unsatisfiable for theBenchmark
% 13.87/12.43
% 13.87/12.43 % Proof 1 at 1.61 (+ 0.37) seconds.
% 13.87/12.43 % Length of proof is 38.
% 13.87/12.43 % Level of proof is 15.
% 13.87/12.43 % Maximum clause weight is 55.000.
% 13.87/12.43 % Given clauses 88.
% 13.87/12.43
% 13.87/12.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------