%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP748-5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 07:31:22 AM UTC 2026
% Result : Unsatisfiable 11.58s 3.78s
% Output : CNFRefutation 11.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 9
% Syntax : Number of formulae : 59 ( 44 unt; 0 def)
% Number of atoms : 76 ( 75 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 2 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 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 : 119 ( 0 sgn 15 !; 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(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(mult(a,b),mult(c,a)) != mult(a,mult(mult(b,c),a)),
file('theBenchmark.p',goals) ).
cnf(c_12,plain,
mult(mult(a,b),mult(c,a)) != mult(a,mult(mult(b,c),a)),
inference(clausify,[status(thm)],[goals]) ).
cnf(c_13,plain,
ld(rd(A,B),A) = B,
inference(paramod,[status(thm)],[c_3,c_2]) ).
cnf(c_4015,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_22,plain,
mult(rd(A,B),mult(mult(B,C),B)) = mult(mult(A,C),B),
inference(copy,[status(thm)],[c_4015]) ).
cnf(c_28,plain,
ld(mult(A,B),A) = i(B),
inference(paramod,[status(thm)],[c_8,c_2]) ).
cnf(c_4016,plain,
mult(A,i(B)) = rd(A,B),
inference(paramod,[status(thm)],[c_3,c_8]) ).
cnf(c_29,plain,
rd(A,B) = mult(A,i(B)),
inference(copy,[status(thm)],[c_4016]) ).
cnf(c_34,plain,
mult(mult(A,i(B)),mult(mult(B,C),B)) = mult(mult(A,C),B),
inference(paramod,[status(thm)],[c_29,c_22]) ).
cnf(c_4017,plain,
ld(mult(A,i(B)),A) = B,
inference(paramod,[status(thm)],[c_29,c_13]) ).
cnf(c_35,plain,
i(i(A)) = A,
inference(paramod,[status(thm)],[c_28,c_4017]) ).
cnf(c_4018,plain,
mult(mult(unit,A),B) = mult(i(B),mult(mult(B,A),B)),
inference(paramod,[status(thm)],[c_10,c_7]) ).
cnf(c_4019,plain,
mult(A,B) = mult(i(B),mult(mult(B,A),B)),
inference(paramod,[status(thm)],[c_6,c_4018]) ).
cnf(c_41,plain,
mult(i(A),mult(mult(A,B),A)) = mult(B,A),
inference(copy,[status(thm)],[c_4019]) ).
cnf(c_4020,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_4021,plain,
( mult(i(A),B) = ld(A,B)
| B = mult(ld(A,B),A) ),
inference(paramod,[status(thm)],[c_1,c_4020]) ).
cnf(c_4022,plain,
( mult(i(A),B) = ld(A,B)
| mult(ld(A,B),A) = B ),
inference(copy,[status(thm)],[c_4021]) ).
cnf(c_42,plain,
( ld(A,B) = mult(i(A),B)
| mult(ld(A,B),A) = B ),
inference(copy,[status(thm)],[c_4022]) ).
cnf(c_4023,plain,
( mult(B,i(A)) = ld(A,B)
| ld(A,B) = mult(i(A),B) ),
inference(paramod,[status(thm)],[c_42,c_8]) ).
cnf(c_68,plain,
( ld(A,B) = mult(B,i(A))
| ld(A,B) = mult(i(A),B) ),
inference(copy,[status(thm)],[c_4023]) ).
cnf(c_4024,plain,
( ld(i(A),B) = mult(B,i(i(A)))
| ld(i(A),B) = mult(A,B) ),
inference(paramod,[status(thm)],[c_35,c_68]) ).
cnf(c_149,plain,
( ld(i(A),B) = mult(B,A)
| ld(i(A),B) = mult(A,B) ),
inference(paramod,[status(thm)],[c_35,c_4024]) ).
cnf(c_4025,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_42,c_149]) ).
cnf(c_4026,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_4025]) ).
cnf(c_180,plain,
( ld(i(A),ld(A,B)) = B
| ld(A,B) = mult(i(A),B) ),
inference(copy,[status(thm)],[c_4026]) ).
cnf(c_1650,plain,
ld(mult(A,i(B)),mult(mult(A,C),B)) = mult(mult(B,C),B),
inference(paramod,[status(thm)],[c_34,c_2]) ).
cnf(c_4027,plain,
( mult(i(A),B) = ld(A,B)
| ld(A,B) = mult(i(A),B) ),
inference(paramod,[status(thm)],[c_180,c_1]) ).
cnf(c_4028,plain,
( ld(A,B) = mult(i(A),B)
| ld(A,B) = mult(i(A),B) ),
inference(copy,[status(thm)],[c_4027]) ).
cnf(c_2778,plain,
ld(A,B) = mult(i(A),B),
inference(copy,[status(thm)],[c_4028]) ).
cnf(c_3005,plain,
mult(i(mult(A,i(B))),mult(mult(A,C),B)) = mult(mult(B,C),B),
inference(paramod,[status(thm)],[c_2778,c_1650]) ).
cnf(c_3199,plain,
mult(i(mult(A,B)),A) = i(B),
inference(paramod,[status(thm)],[c_2778,c_28]) ).
cnf(c_3202,plain,
mult(i(A),mult(A,B)) = B,
inference(paramod,[status(thm)],[c_2778,c_2]) ).
cnf(c_4029,plain,
mult(i(A),i(B)) = i(mult(B,A)),
inference(paramod,[status(thm)],[c_3199,c_8]) ).
cnf(c_3251,plain,
i(mult(A,B)) = mult(i(B),i(A)),
inference(copy,[status(thm)],[c_4029]) ).
cnf(c_4030,plain,
mult(mult(i(i(B)),i(A)),mult(mult(A,C),B)) = mult(mult(B,C),B),
inference(paramod,[status(thm)],[c_3251,c_3005]) ).
cnf(c_3281,plain,
mult(mult(A,i(B)),mult(mult(B,C),A)) = mult(mult(A,C),A),
inference(paramod,[status(thm)],[c_35,c_4030]) ).
cnf(c_4031,plain,
mult(i(i(A)),mult(B,A)) = mult(mult(A,B),A),
inference(paramod,[status(thm)],[c_41,c_3202]) ).
cnf(c_4032,plain,
mult(A,mult(B,A)) = mult(mult(A,B),A),
inference(paramod,[status(thm)],[c_35,c_4031]) ).
cnf(c_3310,plain,
mult(mult(A,B),A) = mult(A,mult(B,A)),
inference(copy,[status(thm)],[c_4032]) ).
cnf(c_3318,plain,
mult(mult(A,i(B)),mult(mult(B,C),A)) = mult(A,mult(C,A)),
inference(paramod,[status(thm)],[c_3310,c_3281]) ).
cnf(c_4033,plain,
mult(mult(A,i(i(B))),mult(C,A)) = mult(A,mult(mult(B,C),A)),
inference(paramod,[status(thm)],[c_3202,c_3318]) ).
cnf(c_4013,plain,
mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)),
inference(paramod,[status(thm)],[c_35,c_4033]) ).
cnf(c_4014,plain,
$false,
inference(resolve,[status(thm)],[c_4013,c_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP748-5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.45 % Computer : n010.cluster.edu
% 0.10/0.45 % Model : x86_64 x86_64
% 0.10/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.45 % Memory : 8046.5625MB
% 0.10/0.45 % OS : Linux 6.8.0-71-generic
% 0.10/0.45 % CPULimit : 300
% 0.10/0.45 % WCLimit : 300
% 0.10/0.45 % DateTime : Fri Sep 25 15:44:14 UTC 2026
% 0.10/0.45 % CPUTime :
% 0.10/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.46 % Process 1135380 was started by sandbox on n010,
% 0.10/0.46 % Fri Sep 25 15:44:14 2026
% 0.10/0.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.46
% 0.10/0.46 % From the command line: assign(max_seconds, 300).
% 11.58/3.78
% 11.58/3.78 % Assigning unary symbol i kb_weight 0 and highest precedence (9).
% 11.58/3.78
% 11.58/3.78 % SZS status Unsatisfiable for theBenchmark
% 11.58/3.78
% 11.58/3.78 % Proof 1 at 1.25 (+ 0.19) seconds.
% 11.58/3.78 % Length of proof is 31.
% 11.58/3.78 % Level of proof is 11.
% 11.58/3.78 % Maximum clause weight is 57.000.
% 11.58/3.78 % Given clauses 141.
% 11.58/3.78
% 11.58/3.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------