%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP748-2 : 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 : n015.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 12.99s 2.13s
% Output : CNFRefutation 12.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 10
% Syntax : Number of formulae : 79 ( 64 unt; 0 def)
% Number of atoms : 96 ( 95 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 4 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 5 ( 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 : 162 ( 0 sgn 16 !; 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(f06,axiom,
! [VAR_0] : mult(unit,VAR_0) = VAR_0,
file('theBenchmark.p',f06) ).
cnf(c_6,plain,
mult(unit,A) = A,
inference(clausify,[status(thm)],[f06]) ).
fof(f07,axiom,
! [VAR_0,VAR_1,VAR_2] : mult(mult(mult(VAR_0,VAR_1),VAR_2),VAR_1) = mult(VAR_0,mult(mult(VAR_1,VAR_2),VAR_1)),
file('theBenchmark.p',f07) ).
cnf(c_7,plain,
mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B)),
inference(clausify,[status(thm)],[f07]) ).
fof(f08,axiom,
! [VAR_0,VAR_1] : mult(mult(VAR_0,VAR_1),i(VAR_1)) = VAR_0,
file('theBenchmark.p',f08) ).
cnf(c_8,plain,
mult(mult(A,B),i(B)) = A,
inference(clausify,[status(thm)],[f08]) ).
fof(f09,axiom,
! [VAR_0] : mult(VAR_0,i(VAR_0)) = unit,
file('theBenchmark.p',f09) ).
cnf(c_9,plain,
mult(A,i(A)) = unit,
inference(clausify,[status(thm)],[f09]) ).
fof(f10,axiom,
! [VAR_0] : mult(i(VAR_0),VAR_0) = unit,
file('theBenchmark.p',f10) ).
cnf(c_10,plain,
mult(i(A),A) = unit,
inference(clausify,[status(thm)],[f10]) ).
fof(f11,axiom,
! [VAR_0,VAR_1] :
( mult(i(VAR_0),mult(VAR_0,VAR_1)) = VAR_1
| mult(VAR_0,VAR_1) = mult(VAR_1,VAR_0) ),
file('theBenchmark.p',f11) ).
cnf(c_11,plain,
( mult(i(A),mult(A,B)) = B
| mult(A,B) = mult(B,A) ),
inference(clausify,[status(thm)],[f11]) ).
fof(goals,axiom,
mult(a,mult(b,mult(a,c))) != mult(mult(mult(a,b),a),c),
file('theBenchmark.p',goals) ).
cnf(c_12,plain,
mult(a,mult(b,mult(a,c))) != mult(mult(mult(a,b),a),c),
inference(clausify,[status(thm)],[goals]) ).
cnf(c_13,plain,
mult(mult(mult(a,b),a),c) != mult(a,mult(b,mult(a,c))),
inference(copy,[status(thm)],[c_12]) ).
cnf(c_14,plain,
ld(rd(A,B),A) = B,
inference(paramod,[status(thm)],[c_3,c_2]) ).
cnf(c_4229,plain,
mult(mult(A,B),C) = mult(rd(A,C),mult(mult(C,B),C)),
inference(paramod,[status(thm)],[c_3,c_7]) ).
cnf(c_23,plain,
mult(rd(A,B),mult(mult(B,C),B)) = mult(mult(A,C),B),
inference(copy,[status(thm)],[c_4229]) ).
cnf(c_29,plain,
ld(mult(A,B),A) = i(B),
inference(paramod,[status(thm)],[c_8,c_2]) ).
cnf(c_4230,plain,
mult(A,i(B)) = rd(A,B),
inference(paramod,[status(thm)],[c_3,c_8]) ).
cnf(c_30,plain,
rd(A,B) = mult(A,i(B)),
inference(copy,[status(thm)],[c_4230]) ).
cnf(c_34,plain,
mult(mult(A,mult(mult(B,C),B)),i(B)) = mult(mult(A,B),C),
inference(paramod,[status(thm)],[c_7,c_8]) ).
cnf(c_35,plain,
mult(mult(A,i(B)),mult(mult(B,C),B)) = mult(mult(A,C),B),
inference(paramod,[status(thm)],[c_30,c_23]) ).
cnf(c_4231,plain,
ld(mult(A,i(B)),A) = B,
inference(paramod,[status(thm)],[c_30,c_14]) ).
cnf(c_36,plain,
i(i(A)) = A,
inference(paramod,[status(thm)],[c_29,c_4231]) ).
cnf(c_4232,plain,
mult(mult(unit,A),i(B)) = mult(B,mult(mult(i(B),A),i(B))),
inference(paramod,[status(thm)],[c_9,c_7]) ).
cnf(c_4233,plain,
mult(A,i(B)) = mult(B,mult(mult(i(B),A),i(B))),
inference(paramod,[status(thm)],[c_6,c_4232]) ).
cnf(c_40,plain,
mult(A,mult(mult(i(A),B),i(A))) = mult(B,i(A)),
inference(copy,[status(thm)],[c_4233]) ).
cnf(c_4234,plain,
mult(mult(unit,A),B) = mult(i(B),mult(mult(B,A),B)),
inference(paramod,[status(thm)],[c_10,c_7]) ).
cnf(c_4235,plain,
mult(A,B) = mult(i(B),mult(mult(B,A),B)),
inference(paramod,[status(thm)],[c_6,c_4234]) ).
cnf(c_42,plain,
mult(i(A),mult(mult(A,B),A)) = mult(B,A),
inference(copy,[status(thm)],[c_4235]) ).
cnf(c_4236,plain,
( mult(i(A),B) = ld(A,B)
| mult(A,ld(A,B)) = mult(ld(A,B),A) ),
inference(paramod,[status(thm)],[c_1,c_11]) ).
cnf(c_4237,plain,
( mult(i(A),B) = ld(A,B)
| B = mult(ld(A,B),A) ),
inference(paramod,[status(thm)],[c_1,c_4236]) ).
cnf(c_4238,plain,
( mult(i(A),B) = ld(A,B)
| mult(ld(A,B),A) = B ),
inference(copy,[status(thm)],[c_4237]) ).
cnf(c_43,plain,
( ld(A,B) = mult(i(A),B)
| mult(ld(A,B),A) = B ),
inference(copy,[status(thm)],[c_4238]) ).
cnf(c_4239,plain,
( mult(B,i(A)) = ld(A,B)
| ld(A,B) = mult(i(A),B) ),
inference(paramod,[status(thm)],[c_43,c_8]) ).
cnf(c_69,plain,
( ld(A,B) = mult(B,i(A))
| ld(A,B) = mult(i(A),B) ),
inference(copy,[status(thm)],[c_4239]) ).
cnf(c_4240,plain,
( ld(i(A),B) = mult(B,i(i(A)))
| ld(i(A),B) = mult(A,B) ),
inference(paramod,[status(thm)],[c_36,c_69]) ).
cnf(c_150,plain,
( ld(i(A),B) = mult(B,A)
| ld(i(A),B) = mult(A,B) ),
inference(paramod,[status(thm)],[c_36,c_4240]) ).
cnf(c_4241,plain,
( ld(i(A),ld(A,B)) = B
| ld(i(A),ld(A,B)) = mult(A,ld(A,B))
| ld(A,B) = mult(i(A),B) ),
inference(paramod,[status(thm)],[c_43,c_150]) ).
cnf(c_4242,plain,
( ld(i(A),ld(A,B)) = B
| ld(i(A),ld(A,B)) = B
| ld(A,B) = mult(i(A),B) ),
inference(paramod,[status(thm)],[c_1,c_4241]) ).
cnf(c_181,plain,
( ld(i(A),ld(A,B)) = B
| ld(A,B) = mult(i(A),B) ),
inference(copy,[status(thm)],[c_4242]) ).
cnf(c_1336,plain,
mult(mult(A,mult(B,C)),i(C)) = mult(mult(A,C),ld(C,B)),
inference(paramod,[status(thm)],[c_1,c_34]) ).
cnf(c_1651,plain,
ld(mult(A,i(B)),mult(mult(A,C),B)) = mult(mult(B,C),B),
inference(paramod,[status(thm)],[c_35,c_2]) ).
cnf(c_4243,plain,
mult(A,mult(B,i(A))) = mult(ld(i(A),B),i(A)),
inference(paramod,[status(thm)],[c_1,c_40]) ).
cnf(c_2245,plain,
mult(ld(i(A),B),i(A)) = mult(A,mult(B,i(A))),
inference(copy,[status(thm)],[c_4243]) ).
cnf(c_4244,plain,
( mult(i(A),B) = ld(A,B)
| ld(A,B) = mult(i(A),B) ),
inference(paramod,[status(thm)],[c_181,c_1]) ).
cnf(c_4245,plain,
( ld(A,B) = mult(i(A),B)
| ld(A,B) = mult(i(A),B) ),
inference(copy,[status(thm)],[c_4244]) ).
cnf(c_2779,plain,
ld(A,B) = mult(i(A),B),
inference(copy,[status(thm)],[c_4245]) ).
cnf(c_4246,plain,
mult(mult(i(i(A)),B),i(A)) = mult(A,mult(B,i(A))),
inference(paramod,[status(thm)],[c_2779,c_2245]) ).
cnf(c_2892,plain,
mult(mult(A,B),i(A)) = mult(A,mult(B,i(A))),
inference(paramod,[status(thm)],[c_36,c_4246]) ).
cnf(c_3006,plain,
mult(i(mult(A,i(B))),mult(mult(A,C),B)) = mult(mult(B,C),B),
inference(paramod,[status(thm)],[c_2779,c_1651]) ).
cnf(c_3079,plain,
mult(mult(A,mult(B,C)),i(C)) = mult(mult(A,C),mult(i(C),B)),
inference(paramod,[status(thm)],[c_2779,c_1336]) ).
cnf(c_3200,plain,
mult(i(mult(A,B)),A) = i(B),
inference(paramod,[status(thm)],[c_2779,c_29]) ).
cnf(c_3203,plain,
mult(i(A),mult(A,B)) = B,
inference(paramod,[status(thm)],[c_2779,c_2]) ).
cnf(c_4247,plain,
mult(i(A),i(B)) = i(mult(B,A)),
inference(paramod,[status(thm)],[c_3200,c_8]) ).
cnf(c_3252,plain,
i(mult(A,B)) = mult(i(B),i(A)),
inference(copy,[status(thm)],[c_4247]) ).
cnf(c_4248,plain,
mult(mult(i(i(B)),i(A)),mult(mult(A,C),B)) = mult(mult(B,C),B),
inference(paramod,[status(thm)],[c_3252,c_3006]) ).
cnf(c_3282,plain,
mult(mult(A,i(B)),mult(mult(B,C),A)) = mult(mult(A,C),A),
inference(paramod,[status(thm)],[c_36,c_4248]) ).
cnf(c_4249,plain,
mult(i(i(A)),mult(B,A)) = mult(mult(A,B),A),
inference(paramod,[status(thm)],[c_42,c_3203]) ).
cnf(c_4250,plain,
mult(A,mult(B,A)) = mult(mult(A,B),A),
inference(paramod,[status(thm)],[c_36,c_4249]) ).
cnf(c_3311,plain,
mult(mult(A,B),A) = mult(A,mult(B,A)),
inference(copy,[status(thm)],[c_4250]) ).
cnf(c_3319,plain,
mult(mult(A,i(B)),mult(mult(B,C),A)) = mult(A,mult(C,A)),
inference(paramod,[status(thm)],[c_3311,c_3282]) ).
cnf(c_3348,plain,
mult(mult(a,mult(b,a)),c) != mult(a,mult(b,mult(a,c))),
inference(paramod,[status(thm)],[c_3311,c_13]) ).
cnf(c_4251,plain,
mult(mult(A,i(i(B))),mult(C,A)) = mult(A,mult(mult(B,C),A)),
inference(paramod,[status(thm)],[c_3203,c_3319]) ).
cnf(c_4015,plain,
mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)),
inference(paramod,[status(thm)],[c_36,c_4251]) ).
cnf(c_4252,plain,
mult(mult(mult(A,B),mult(C,A)),i(A)) = mult(mult(A,mult(B,A)),mult(i(A),C)),
inference(paramod,[status(thm)],[c_3311,c_3079]) ).
cnf(c_4253,plain,
mult(mult(A,mult(mult(B,C),A)),i(A)) = mult(mult(A,mult(B,A)),mult(i(A),C)),
inference(paramod,[status(thm)],[c_4015,c_4252]) ).
cnf(c_4254,plain,
mult(A,mult(mult(mult(B,C),A),i(A))) = mult(mult(A,mult(B,A)),mult(i(A),C)),
inference(paramod,[status(thm)],[c_2892,c_4253]) ).
cnf(c_4255,plain,
mult(A,mult(B,C)) = mult(mult(A,mult(B,A)),mult(i(A),C)),
inference(paramod,[status(thm)],[c_8,c_4254]) ).
cnf(c_4160,plain,
mult(mult(A,mult(B,A)),mult(i(A),C)) = mult(A,mult(B,C)),
inference(copy,[status(thm)],[c_4255]) ).
cnf(c_4227,plain,
mult(mult(A,mult(B,A)),C) = mult(A,mult(B,mult(A,C))),
inference(paramod,[status(thm)],[c_3203,c_4160]) ).
cnf(c_4228,plain,
$false,
inference(resolve,[status(thm)],[c_4227,c_3348]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP748-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n015.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 15:46:42 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.36 % Process 1743298 was started by sandbox2 on n015,
% 0.14/0.36 % Fri Sep 25 15:46:42 2026
% 0.14/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.37
% 0.14/0.37 % From the command line: assign(max_seconds, 300).
% 12.99/2.13
% 12.99/2.13 % Assigning unary symbol i kb_weight 0 and highest precedence (9).
% 12.99/2.13
% 12.99/2.13 % SZS status Unsatisfiable for theBenchmark
% 12.99/2.13
% 12.99/2.13 % Proof 1 at 1.38 (+ 0.26) seconds.
% 12.99/2.13 % Length of proof is 42.
% 12.99/2.13 % Level of proof is 13.
% 12.99/2.13 % Maximum clause weight is 61.000.
% 12.99/2.13 % Given clauses 146.
% 12.99/2.13
% 12.99/2.13 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------