%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP703-11 : 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 : 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 07:31:16 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.47s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 51 ( 51 unt; 0 def)
% Number of atoms : 51 ( 50 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 9 ( 9 ~; 0 |; 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn 18 !; 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(f07,axiom,
! [VAR_0,VAR_1,VAR_2] : mult(VAR_0,mult(VAR_1,mult(VAR_1,VAR_2))) = mult(mult(mult(VAR_0,VAR_1),VAR_1),VAR_2),
file('theBenchmark.p',f07) ).
cnf(c_7,plain,
mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C),
inference(clausify,[status(thm)],[f07]) ).
cnf(c_8,plain,
mult(mult(mult(A,B),B),C) = mult(A,mult(B,mult(B,C))),
inference(copy,[status(thm)],[c_7]) ).
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(x3,op_e)) != mult(mult(x2,x3),op_e),
file('theBenchmark.p',goal) ).
cnf(c_21,plain,
mult(x2,mult(x3,op_e)) != mult(mult(x2,x3),op_e),
inference(clausify,[status(thm)],[goal]) ).
cnf(c_22,plain,
mult(mult(x2,x3),op_e) != mult(x2,mult(x3,op_e)),
inference(copy,[status(thm)],[c_21]) ).
cnf(c_112,plain,
mult(mult(A,B),C) = mult(rd(A,B),mult(B,mult(B,C))),
inference(paramod,[status(thm)],[c_3,c_8]) ).
cnf(c_32,plain,
mult(rd(A,B),mult(B,mult(B,C))) = mult(mult(A,B),C),
inference(copy,[status(thm)],[c_112]) ).
cnf(c_113,plain,
mult(A,B) = mult(rd(A,op_c),mult(op_c,B)),
inference(paramod,[status(thm)],[c_3,c_14]) ).
cnf(c_56,plain,
mult(rd(A,op_c),mult(op_c,B)) = mult(A,B),
inference(copy,[status(thm)],[c_113]) ).
cnf(c_114,plain,
mult(A,op_d) = mult(op_c,A),
inference(paramod,[status(thm)],[c_16,c_1]) ).
cnf(c_59,plain,
mult(op_c,A) = mult(A,op_d),
inference(copy,[status(thm)],[c_114]) ).
cnf(c_61,plain,
op_d = op_c,
inference(paramod,[status(thm)],[c_16,c_2]) ).
cnf(c_63,plain,
mult(op_c,A) = mult(A,op_c),
inference(paramod,[status(thm)],[c_61,c_59]) ).
cnf(c_115,plain,
op_e = mult(rd(op_c,mult(unit,A)),A),
inference(paramod,[status(thm)],[c_18,c_5]) ).
cnf(c_116,plain,
op_e = mult(rd(op_c,A),A),
inference(paramod,[status(thm)],[c_6,c_115]) ).
cnf(c_72,plain,
op_e = op_c,
inference(paramod,[status(thm)],[c_3,c_116]) ).
cnf(c_117,plain,
mult(mult(x2,x3),op_c) != mult(x2,mult(x3,op_e)),
inference(paramod,[status(thm)],[c_72,c_22]) ).
cnf(c_118,plain,
mult(op_c,mult(x2,x3)) != mult(x2,mult(x3,op_e)),
inference(paramod,[status(thm)],[c_63,c_117]) ).
cnf(c_119,plain,
mult(op_c,mult(x2,x3)) != mult(x2,mult(x3,op_c)),
inference(paramod,[status(thm)],[c_72,c_118]) ).
cnf(c_120,plain,
mult(op_c,mult(x2,x3)) != mult(x2,mult(op_c,x3)),
inference(paramod,[status(thm)],[c_63,c_119]) ).
cnf(c_82,plain,
mult(x2,mult(op_c,x3)) != mult(op_c,mult(x2,x3)),
inference(copy,[status(thm)],[c_120]) ).
cnf(c_121,plain,
mult(mult(rd(A,op_c),op_c),mult(op_c,B)) = mult(mult(A,op_c),B),
inference(paramod,[status(thm)],[c_32,c_14]) ).
cnf(c_122,plain,
mult(mult(op_c,rd(A,op_c)),mult(op_c,B)) = mult(mult(A,op_c),B),
inference(paramod,[status(thm)],[c_63,c_121]) ).
cnf(c_123,plain,
mult(op_c,mult(rd(A,op_c),mult(op_c,B))) = mult(mult(A,op_c),B),
inference(paramod,[status(thm)],[c_10,c_122]) ).
cnf(c_124,plain,
mult(op_c,mult(A,B)) = mult(mult(A,op_c),B),
inference(paramod,[status(thm)],[c_56,c_123]) ).
cnf(c_110,plain,
mult(op_c,mult(A,B)) = mult(A,mult(op_c,B)),
inference(paramod,[status(thm)],[c_14,c_124]) ).
cnf(c_125,plain,
mult(op_c,mult(x2,x3)) != mult(x2,mult(op_c,x3)),
inference(copy,[status(thm)],[c_82]) ).
cnf(c_111,plain,
$false,
inference(resolve,[status(thm)],[c_110,c_125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP703-11 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n010.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Fri Sep 25 15:39:18 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.44 % Process 1126657 was started by sandbox2 on n010,
% 0.16/0.44 % Fri Sep 25 15:39:18 2026
% 0.16/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.45
% 0.16/0.45 % From the command line: assign(max_seconds, 300).
% 0.16/0.47
% 0.16/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.47
% 0.16/0.47 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.16/0.47 % Length of proof is 26.
% 0.16/0.47 % Level of proof is 5.
% 0.16/0.47 % Maximum clause weight is 55.000.
% 0.16/0.47 % Given clauses 25.
% 0.16/0.47
% 0.16/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------