%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP703-12 : 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 : n016.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 07:31:16 AM UTC 2026
% Result : Unsatisfiable 0.38s 15.52s
% Output : CNFRefutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 42 ( 42 unt; 0 def)
% Number of atoms : 42 ( 41 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 9 ( 9 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 48 ( 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(f05,axiom,
! [VAR_0] : mult(VAR_0,unit) = VAR_0,
file('theBenchmark.p',f05) ).
cnf(c_5,plain,
mult(A,unit) = A,
inference(clausify,[status(thm)],[f05]) ).
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(f08,axiom,
! [VAR_0,VAR_1] : mult(op_c,mult(VAR_0,VAR_1)) = mult(mult(op_c,VAR_0),VAR_1),
file('theBenchmark.p',f08) ).
cnf(c_9,plain,
mult(op_c,mult(A,B)) = mult(mult(op_c,A),B),
inference(clausify,[status(thm)],[f08]) ).
cnf(c_10,plain,
mult(mult(op_c,A),B) = mult(op_c,mult(A,B)),
inference(copy,[status(thm)],[c_9]) ).
fof(f10,axiom,
! [VAR_0,VAR_1] : mult(VAR_0,mult(op_c,VAR_1)) = mult(mult(VAR_0,op_c),VAR_1),
file('theBenchmark.p',f10) ).
cnf(c_13,plain,
mult(A,mult(op_c,B)) = mult(mult(A,op_c),B),
inference(clausify,[status(thm)],[f10]) ).
cnf(c_14,plain,
mult(mult(A,op_c),B) = mult(A,mult(op_c,B)),
inference(copy,[status(thm)],[c_13]) ).
fof(f11,axiom,
! [VAR_0] : op_d = ld(VAR_0,mult(op_c,VAR_0)),
file('theBenchmark.p',f11) ).
cnf(c_15,plain,
op_d = ld(A,mult(op_c,A)),
inference(clausify,[status(thm)],[f11]) ).
cnf(c_16,plain,
ld(A,mult(op_c,A)) = op_d,
inference(copy,[status(thm)],[c_15]) ).
fof(f12,axiom,
! [VAR_0,VAR_1] : op_e = mult(mult(rd(op_c,mult(VAR_0,VAR_1)),VAR_1),VAR_0),
file('theBenchmark.p',f12) ).
cnf(c_17,plain,
op_e = mult(mult(rd(op_c,mult(A,B)),B),A),
inference(clausify,[status(thm)],[f12]) ).
cnf(c_18,plain,
mult(mult(rd(op_c,mult(A,B)),B),A) = op_e,
inference(copy,[status(thm)],[c_17]) ).
fof(goal,axiom,
mult(x2,mult(op_e,x3)) != mult(mult(x2,op_e),x3),
file('theBenchmark.p',goal) ).
cnf(c_21,plain,
mult(x2,mult(op_e,x3)) != mult(mult(x2,op_e),x3),
inference(clausify,[status(thm)],[goal]) ).
cnf(c_22,plain,
mult(mult(x2,op_e),x3) != mult(x2,mult(op_e,x3)),
inference(copy,[status(thm)],[c_21]) ).
cnf(c_115,plain,
mult(A,op_d) = mult(op_c,A),
inference(paramod,[status(thm)],[c_16,c_1]) ).
cnf(c_62,plain,
mult(op_c,A) = mult(A,op_d),
inference(copy,[status(thm)],[c_115]) ).
cnf(c_64,plain,
op_d = op_c,
inference(paramod,[status(thm)],[c_16,c_2]) ).
cnf(c_66,plain,
mult(op_c,A) = mult(A,op_c),
inference(paramod,[status(thm)],[c_64,c_62]) ).
cnf(c_116,plain,
op_e = mult(rd(op_c,mult(unit,A)),A),
inference(paramod,[status(thm)],[c_18,c_5]) ).
cnf(c_117,plain,
op_e = mult(rd(op_c,A),A),
inference(paramod,[status(thm)],[c_6,c_116]) ).
cnf(c_75,plain,
op_e = op_c,
inference(paramod,[status(thm)],[c_3,c_117]) ).
cnf(c_118,plain,
mult(mult(x2,op_c),x3) != mult(x2,mult(op_e,x3)),
inference(paramod,[status(thm)],[c_75,c_22]) ).
cnf(c_119,plain,
mult(mult(op_c,x2),x3) != mult(x2,mult(op_e,x3)),
inference(paramod,[status(thm)],[c_66,c_118]) ).
cnf(c_120,plain,
mult(op_c,mult(x2,x3)) != mult(x2,mult(op_e,x3)),
inference(paramod,[status(thm)],[c_10,c_119]) ).
cnf(c_121,plain,
mult(op_c,mult(x2,x3)) != mult(x2,mult(op_c,x3)),
inference(paramod,[status(thm)],[c_75,c_120]) ).
cnf(c_85,plain,
mult(x2,mult(op_c,x3)) != mult(op_c,mult(x2,x3)),
inference(copy,[status(thm)],[c_121]) ).
cnf(c_122,plain,
mult(mult(A,op_c),B) = mult(op_c,mult(A,B)),
inference(paramod,[status(thm)],[c_66,c_10]) ).
cnf(c_123,plain,
mult(A,mult(op_c,B)) = mult(op_c,mult(A,B)),
inference(paramod,[status(thm)],[c_14,c_122]) ).
cnf(c_113,plain,
mult(op_c,mult(A,B)) = mult(A,mult(op_c,B)),
inference(copy,[status(thm)],[c_123]) ).
cnf(c_124,plain,
mult(op_c,mult(x2,x3)) != mult(x2,mult(op_c,x3)),
inference(copy,[status(thm)],[c_85]) ).
cnf(c_114,plain,
$false,
inference(resolve,[status(thm)],[c_113,c_124]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP703-12 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.15/15.49 % CPULimit : 300
% 0.15/15.49 % WCLimit : 300
% 0.15/15.50 % DateTime : Fri Sep 25 15:38:38 UTC 2026
% 0.38/15.50 % CPUTime :
% 0.38/15.50 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.38/15.50 % Process 751243 was started by sandbox2 on n013,
% 0.38/15.50 % Fri Sep 25 15:38:38 2026
% 0.38/15.50 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.38/15.51
% 0.38/15.51 % From the command line: assign(max_seconds, 300).
% 0.38/15.52
% 0.38/15.52 % SZS status Unsatisfiable for theBenchmark
% 0.38/15.52
% 0.38/15.52 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.38/15.52 % Length of proof is 22.
% 0.38/15.52 % Level of proof is 5.
% 0.38/15.52 % Maximum clause weight is 11.000.
% 0.38/15.52 % Given clauses 26.
% 0.38/15.52
% 0.38/15.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------