%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP748-3 : 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 14.58s 7.37s
% Output : CNFRefutation 14.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 9
% Syntax : Number of formulae : 49 ( 34 unt; 0 def)
% Number of atoms : 66 ( 65 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 5 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 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 : 83 ( 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(a,mult(b,mult(c,b))) != mult(mult(mult(a,b),c),b),
file('theBenchmark.p',goals) ).
cnf(c_12,plain,
mult(a,mult(b,mult(c,b))) != mult(mult(mult(a,b),c),b),
inference(clausify,[status(thm)],[goals]) ).
cnf(c_3349,plain,
mult(a,mult(b,mult(c,b))) != mult(a,mult(mult(b,c),b)),
inference(paramod,[status(thm)],[c_7,c_12]) ).
cnf(c_13,plain,
mult(a,mult(mult(b,c),b)) != mult(a,mult(b,mult(c,b))),
inference(copy,[status(thm)],[c_3349]) ).
cnf(c_14,plain,
ld(rd(A,B),A) = B,
inference(paramod,[status(thm)],[c_3,c_2]) ).
cnf(c_29,plain,
ld(mult(A,B),A) = i(B),
inference(paramod,[status(thm)],[c_8,c_2]) ).
cnf(c_3350,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_3350]) ).
cnf(c_3351,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_3351]) ).
cnf(c_3352,plain,
mult(mult(unit,A),B) = mult(i(B),mult(mult(B,A),B)),
inference(paramod,[status(thm)],[c_10,c_7]) ).
cnf(c_3353,plain,
mult(A,B) = mult(i(B),mult(mult(B,A),B)),
inference(paramod,[status(thm)],[c_6,c_3352]) ).
cnf(c_42,plain,
mult(i(A),mult(mult(A,B),A)) = mult(B,A),
inference(copy,[status(thm)],[c_3353]) ).
cnf(c_3354,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_3355,plain,
( mult(i(A),B) = ld(A,B)
| B = mult(ld(A,B),A) ),
inference(paramod,[status(thm)],[c_1,c_3354]) ).
cnf(c_3356,plain,
( mult(i(A),B) = ld(A,B)
| mult(ld(A,B),A) = B ),
inference(copy,[status(thm)],[c_3355]) ).
cnf(c_43,plain,
( ld(A,B) = mult(i(A),B)
| mult(ld(A,B),A) = B ),
inference(copy,[status(thm)],[c_3356]) ).
cnf(c_3357,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_3357]) ).
cnf(c_3358,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_3358]) ).
cnf(c_3359,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_3360,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_3359]) ).
cnf(c_181,plain,
( ld(i(A),ld(A,B)) = B
| ld(A,B) = mult(i(A),B) ),
inference(copy,[status(thm)],[c_3360]) ).
cnf(c_3361,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_3362,plain,
( ld(A,B) = mult(i(A),B)
| ld(A,B) = mult(i(A),B) ),
inference(copy,[status(thm)],[c_3361]) ).
cnf(c_2779,plain,
ld(A,B) = mult(i(A),B),
inference(copy,[status(thm)],[c_3362]) ).
cnf(c_3203,plain,
mult(i(A),mult(A,B)) = B,
inference(paramod,[status(thm)],[c_2779,c_2]) ).
cnf(c_3363,plain,
mult(i(i(A)),mult(B,A)) = mult(mult(A,B),A),
inference(paramod,[status(thm)],[c_42,c_3203]) ).
cnf(c_3364,plain,
mult(A,mult(B,A)) = mult(mult(A,B),A),
inference(paramod,[status(thm)],[c_36,c_3363]) ).
cnf(c_3311,plain,
mult(mult(A,B),A) = mult(A,mult(B,A)),
inference(copy,[status(thm)],[c_3364]) ).
cnf(c_3365,plain,
mult(a,mult(b,mult(c,b))) != mult(a,mult(b,mult(c,b))),
inference(paramod,[status(thm)],[c_3311,c_13]) ).
cnf(c_3348,plain,
$false,
inference(copy,[status(thm)],[c_3365]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP748-3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/5.45 % Computer : n001.cluster.edu
% 0.19/5.45 % Model : x86_64 x86_64
% 0.19/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.45 % Memory : 8046.5625MB
% 0.19/5.45 % OS : Linux 6.8.0-71-generic
% 0.19/5.45 % CPULimit : 300
% 0.19/5.45 % WCLimit : 300
% 0.19/5.45 % DateTime : Fri Sep 25 15:49:01 UTC 2026
% 0.19/5.46 % CPUTime :
% 0.19/5.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/5.46 % Process 3735531 was started by sandbox2 on n001,
% 0.19/5.46 % Fri Sep 25 15:49:01 2026
% 0.19/5.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/5.46
% 0.19/5.46 % From the command line: assign(max_seconds, 300).
% 14.58/7.37
% 14.58/7.37 % Assigning unary symbol i kb_weight 0 and highest precedence (9).
% 14.58/7.37
% 14.58/7.37 % SZS status Unsatisfiable for theBenchmark
% 14.58/7.37
% 14.58/7.37 % Proof 1 at 1.64 (+ 0.24) seconds.
% 14.58/7.37 % Length of proof is 23.
% 14.58/7.37 % Level of proof is 8.
% 14.58/7.37 % Maximum clause weight is 55.000.
% 14.58/7.37 % Given clauses 97.
% 14.58/7.37
% 14.58/7.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------