%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP728-1 : 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 : 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 07:31:20 AM UTC 2026
% Result : Unsatisfiable 3.24s 1.22s
% Output : CNFRefutation 3.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 12
% Syntax : Number of formulae : 73 ( 73 unt; 0 def)
% Number of atoms : 73 ( 72 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 163 ( 31 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(c01,axiom,
! [VAR_0] : mult(unit,VAR_0) = VAR_0,
file('theBenchmark.p',c01) ).
cnf(c_1,plain,
mult(unit,A) = A,
inference(clausify,[status(thm)],[c01]) ).
fof(c02,axiom,
! [VAR_0] : mult(VAR_0,unit) = VAR_0,
file('theBenchmark.p',c02) ).
cnf(c_2,plain,
mult(A,unit) = A,
inference(clausify,[status(thm)],[c02]) ).
fof(c03,axiom,
! [VAR_0] : mult(VAR_0,i(VAR_0)) = unit,
file('theBenchmark.p',c03) ).
cnf(c_3,plain,
mult(A,i(A)) = unit,
inference(clausify,[status(thm)],[c03]) ).
fof(c04,axiom,
! [VAR_0] : mult(i(VAR_0),VAR_0) = unit,
file('theBenchmark.p',c04) ).
cnf(c_4,plain,
mult(i(A),A) = unit,
inference(clausify,[status(thm)],[c04]) ).
fof(c05,axiom,
! [VAR_0,VAR_1] : i(mult(VAR_0,VAR_1)) = mult(i(VAR_0),i(VAR_1)),
file('theBenchmark.p',c05) ).
cnf(c_5,plain,
i(mult(A,B)) = mult(i(A),i(B)),
inference(clausify,[status(thm)],[c05]) ).
fof(c06,axiom,
! [VAR_0,VAR_1] : mult(i(VAR_0),mult(VAR_0,VAR_1)) = VAR_1,
file('theBenchmark.p',c06) ).
cnf(c_6,plain,
mult(i(A),mult(A,B)) = B,
inference(clausify,[status(thm)],[c06]) ).
fof(c07,axiom,
! [VAR_0,VAR_1] : rd(mult(VAR_0,VAR_1),VAR_1) = VAR_0,
file('theBenchmark.p',c07) ).
cnf(c_7,plain,
rd(mult(A,B),B) = A,
inference(clausify,[status(thm)],[c07]) ).
fof(c10,axiom,
! [VAR_0,VAR_1,VAR_2] : mult(mult(VAR_0,VAR_1),VAR_2) = mult(mult(VAR_0,mult(VAR_1,VAR_2)),asoc(VAR_0,VAR_1,VAR_2)),
file('theBenchmark.p',c10) ).
cnf(c_10,plain,
mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)),
inference(clausify,[status(thm)],[c10]) ).
cnf(c_11,plain,
mult(mult(A,mult(B,C)),asoc(A,B,C)) = mult(mult(A,B),C),
inference(copy,[status(thm)],[c_10]) ).
fof(c11,axiom,
! [VAR_0,VAR_1] : mult(VAR_0,VAR_1) = mult(mult(VAR_1,VAR_0),op_k(VAR_0,VAR_1)),
file('theBenchmark.p',c11) ).
cnf(c_12,plain,
mult(A,B) = mult(mult(B,A),op_k(A,B)),
inference(clausify,[status(thm)],[c11]) ).
cnf(c_13,plain,
mult(mult(A,B),op_k(B,A)) = mult(B,A),
inference(copy,[status(thm)],[c_12]) ).
fof(c21,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] : asoc(asoc(VAR_0,VAR_1,VAR_2),VAR_3,VAR_4) = unit,
file('theBenchmark.p',c21) ).
cnf(c_30,plain,
asoc(asoc(A,B,C),D,E) = unit,
inference(clausify,[status(thm)],[c21]) ).
fof(c22,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] : asoc(VAR_0,VAR_1,asoc(VAR_2,VAR_3,VAR_4)) = unit,
file('theBenchmark.p',c22) ).
cnf(c_31,plain,
asoc(A,B,asoc(C,D,E)) = unit,
inference(clausify,[status(thm)],[c22]) ).
fof(goals,axiom,
op_k(op_k(a,b),c) != unit,
file('theBenchmark.p',goals) ).
cnf(c_32,plain,
op_k(op_k(a,b),c) != unit,
inference(clausify,[status(thm)],[goals]) ).
cnf(c_2852,plain,
mult(i(i(A)),unit) = A,
inference(paramod,[status(thm)],[c_4,c_6]) ).
cnf(c_36,plain,
i(i(A)) = A,
inference(paramod,[status(thm)],[c_2,c_2852]) ).
cnf(c_40,plain,
rd(A,unit) = A,
inference(paramod,[status(thm)],[c_2,c_7]) ).
cnf(c_2853,plain,
mult(i(mult(A,mult(B,C))),mult(mult(A,B),C)) = asoc(A,B,C),
inference(paramod,[status(thm)],[c_11,c_6]) ).
cnf(c_2854,plain,
mult(mult(i(A),i(mult(B,C))),mult(mult(A,B),C)) = asoc(A,B,C),
inference(paramod,[status(thm)],[c_5,c_2853]) ).
cnf(c_61,plain,
mult(mult(i(A),mult(i(B),i(C))),mult(mult(A,B),C)) = asoc(A,B,C),
inference(paramod,[status(thm)],[c_5,c_2854]) ).
cnf(c_63,plain,
rd(mult(mult(A,B),C),asoc(A,B,C)) = mult(A,mult(B,C)),
inference(paramod,[status(thm)],[c_11,c_7]) ).
cnf(c_2855,plain,
mult(i(mult(A,B)),mult(B,A)) = op_k(B,A),
inference(paramod,[status(thm)],[c_13,c_6]) ).
cnf(c_77,plain,
mult(mult(i(A),i(B)),mult(B,A)) = op_k(B,A),
inference(paramod,[status(thm)],[c_5,c_2855]) ).
cnf(c_212,plain,
mult(A,mult(i(A),B)) = B,
inference(paramod,[status(thm)],[c_36,c_6]) ).
cnf(c_2856,plain,
mult(mult(i(i(A)),mult(i(i(B)),i(mult(B,A)))),op_k(B,A)) = asoc(i(A),i(B),mult(B,A)),
inference(paramod,[status(thm)],[c_77,c_61]) ).
cnf(c_2857,plain,
mult(mult(A,mult(i(i(B)),i(mult(B,A)))),op_k(B,A)) = asoc(i(A),i(B),mult(B,A)),
inference(paramod,[status(thm)],[c_36,c_2856]) ).
cnf(c_2858,plain,
mult(mult(A,mult(B,i(mult(B,A)))),op_k(B,A)) = asoc(i(A),i(B),mult(B,A)),
inference(paramod,[status(thm)],[c_36,c_2857]) ).
cnf(c_2859,plain,
mult(mult(A,mult(B,mult(i(B),i(A)))),op_k(B,A)) = asoc(i(A),i(B),mult(B,A)),
inference(paramod,[status(thm)],[c_5,c_2858]) ).
cnf(c_2860,plain,
mult(mult(A,i(A)),op_k(B,A)) = asoc(i(A),i(B),mult(B,A)),
inference(paramod,[status(thm)],[c_212,c_2859]) ).
cnf(c_2861,plain,
mult(unit,op_k(B,A)) = asoc(i(A),i(B),mult(B,A)),
inference(paramod,[status(thm)],[c_3,c_2860]) ).
cnf(c_2862,plain,
op_k(B,A) = asoc(i(A),i(B),mult(B,A)),
inference(paramod,[status(thm)],[c_1,c_2861]) ).
cnf(c_2236,plain,
asoc(i(A),i(B),mult(B,A)) = op_k(B,A),
inference(copy,[status(thm)],[c_2862]) ).
cnf(c_2863,plain,
mult(mult(i(mult(A,B)),i(mult(i(B),i(A)))),op_k(A,B)) = op_k(mult(i(B),i(A)),mult(A,B)),
inference(paramod,[status(thm)],[c_77,c_77]) ).
cnf(c_2864,plain,
mult(mult(mult(i(A),i(B)),i(mult(i(B),i(A)))),op_k(A,B)) = op_k(mult(i(B),i(A)),mult(A,B)),
inference(paramod,[status(thm)],[c_5,c_2863]) ).
cnf(c_2865,plain,
mult(mult(mult(i(A),i(B)),mult(i(i(B)),i(i(A)))),op_k(A,B)) = op_k(mult(i(B),i(A)),mult(A,B)),
inference(paramod,[status(thm)],[c_5,c_2864]) ).
cnf(c_2866,plain,
mult(mult(mult(i(A),i(B)),mult(B,i(i(A)))),op_k(A,B)) = op_k(mult(i(B),i(A)),mult(A,B)),
inference(paramod,[status(thm)],[c_36,c_2865]) ).
cnf(c_2867,plain,
mult(mult(mult(i(A),i(B)),mult(B,A)),op_k(A,B)) = op_k(mult(i(B),i(A)),mult(A,B)),
inference(paramod,[status(thm)],[c_36,c_2866]) ).
cnf(c_2868,plain,
mult(op_k(B,A),op_k(A,B)) = op_k(mult(i(B),i(A)),mult(A,B)),
inference(paramod,[status(thm)],[c_77,c_2867]) ).
cnf(c_2245,plain,
op_k(mult(i(A),i(B)),mult(B,A)) = mult(op_k(A,B),op_k(B,A)),
inference(copy,[status(thm)],[c_2868]) ).
cnf(c_2325,plain,
asoc(op_k(A,B),C,D) = unit,
inference(paramod,[status(thm)],[c_2236,c_30]) ).
cnf(c_2326,plain,
asoc(A,B,op_k(C,D)) = unit,
inference(paramod,[status(thm)],[c_2236,c_31]) ).
cnf(c_2869,plain,
asoc(i(mult(A,B)),i(mult(i(B),i(A))),op_k(A,B)) = op_k(mult(i(B),i(A)),mult(A,B)),
inference(paramod,[status(thm)],[c_77,c_2236]) ).
cnf(c_2870,plain,
asoc(mult(i(A),i(B)),i(mult(i(B),i(A))),op_k(A,B)) = op_k(mult(i(B),i(A)),mult(A,B)),
inference(paramod,[status(thm)],[c_5,c_2869]) ).
cnf(c_2871,plain,
asoc(mult(i(A),i(B)),mult(i(i(B)),i(i(A))),op_k(A,B)) = op_k(mult(i(B),i(A)),mult(A,B)),
inference(paramod,[status(thm)],[c_5,c_2870]) ).
cnf(c_2872,plain,
asoc(mult(i(A),i(B)),mult(B,i(i(A))),op_k(A,B)) = op_k(mult(i(B),i(A)),mult(A,B)),
inference(paramod,[status(thm)],[c_36,c_2871]) ).
cnf(c_2873,plain,
asoc(mult(i(A),i(B)),mult(B,A),op_k(A,B)) = op_k(mult(i(B),i(A)),mult(A,B)),
inference(paramod,[status(thm)],[c_36,c_2872]) ).
cnf(c_2874,plain,
unit = op_k(mult(i(B),i(A)),mult(A,B)),
inference(paramod,[status(thm)],[c_2326,c_2873]) ).
cnf(c_2875,plain,
unit = mult(op_k(B,A),op_k(A,B)),
inference(paramod,[status(thm)],[c_2245,c_2874]) ).
cnf(c_2352,plain,
mult(op_k(A,B),op_k(B,A)) = unit,
inference(copy,[status(thm)],[c_2875]) ).
cnf(c_2876,plain,
rd(mult(mult(op_k(A,B),C),D),unit) = mult(op_k(A,B),mult(C,D)),
inference(paramod,[status(thm)],[c_2325,c_63]) ).
cnf(c_2384,plain,
mult(mult(op_k(A,B),C),D) = mult(op_k(A,B),mult(C,D)),
inference(paramod,[status(thm)],[c_40,c_2876]) ).
cnf(c_2877,plain,
mult(i(op_k(A,B)),unit) = op_k(B,A),
inference(paramod,[status(thm)],[c_2352,c_6]) ).
cnf(c_2462,plain,
i(op_k(A,B)) = op_k(B,A),
inference(paramod,[status(thm)],[c_2,c_2877]) ).
cnf(c_2878,plain,
mult(mult(op_k(A,B),i(C)),mult(C,op_k(B,A))) = op_k(C,op_k(B,A)),
inference(paramod,[status(thm)],[c_2462,c_77]) ).
cnf(c_2879,plain,
mult(op_k(A,B),mult(i(C),mult(C,op_k(B,A)))) = op_k(C,op_k(B,A)),
inference(paramod,[status(thm)],[c_2384,c_2878]) ).
cnf(c_2880,plain,
mult(op_k(A,B),op_k(B,A)) = op_k(C,op_k(B,A)),
inference(paramod,[status(thm)],[c_6,c_2879]) ).
cnf(c_2881,plain,
unit = op_k(C,op_k(B,A)),
inference(paramod,[status(thm)],[c_2352,c_2880]) ).
cnf(c_2690,plain,
op_k(A,op_k(B,C)) = unit,
inference(copy,[status(thm)],[c_2881]) ).
cnf(c_2882,plain,
mult(unit,op_k(op_k(A,B),C)) = unit,
inference(paramod,[status(thm)],[c_2690,c_2352]) ).
cnf(c_2850,plain,
op_k(op_k(A,B),C) = unit,
inference(paramod,[status(thm)],[c_1,c_2882]) ).
cnf(c_2851,plain,
$false,
inference(resolve,[status(thm)],[c_2850,c_32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP728-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n001.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 25 15:46:55 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.34 % Process 3726670 was started by sandbox on n001,
% 0.08/0.34 % Fri Sep 25 15:46:55 2026
% 0.08/0.34 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.35
% 0.08/0.35 % From the command line: assign(max_seconds, 300).
% 3.24/1.22
% 3.24/1.22 % Assigning unary symbol i kb_weight 0 and highest precedence (13).
% 3.24/1.22
% 3.24/1.22 % SZS status Unsatisfiable for theBenchmark
% 3.24/1.22
% 3.24/1.22 % Proof 1 at 0.36 (+ 0.11) seconds.
% 3.24/1.22 % Length of proof is 30.
% 3.24/1.22 % Level of proof is 9.
% 3.24/1.22 % Maximum clause weight is 52.000.
% 3.24/1.22 % Given clauses 144.
% 3.24/1.22
% 3.24/1.22 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------