%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP680-1 : 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 : n020.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 07:31:10 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.44s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 51 ( 51 unt; 0 def)
% Number of atoms : 51 ( 50 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(c01,axiom,
! [VAR_0,VAR_1] : mult(VAR_0,ld(VAR_0,VAR_1)) = VAR_1,
file('theBenchmark.p',c01) ).
cnf(c_1,plain,
mult(A,ld(A,B)) = B,
inference(clausify,[status(thm)],[c01]) ).
fof(c02,axiom,
! [VAR_0,VAR_1] : ld(VAR_0,mult(VAR_0,VAR_1)) = VAR_1,
file('theBenchmark.p',c02) ).
cnf(c_2,plain,
ld(A,mult(A,B)) = B,
inference(clausify,[status(thm)],[c02]) ).
fof(c03,axiom,
! [VAR_0,VAR_1] : mult(rd(VAR_0,VAR_1),VAR_1) = VAR_0,
file('theBenchmark.p',c03) ).
cnf(c_3,plain,
mult(rd(A,B),B) = A,
inference(clausify,[status(thm)],[c03]) ).
fof(c04,axiom,
! [VAR_0,VAR_1] : rd(mult(VAR_0,VAR_1),VAR_1) = VAR_0,
file('theBenchmark.p',c04) ).
cnf(c_4,plain,
rd(mult(A,B),B) = A,
inference(clausify,[status(thm)],[c04]) ).
fof(c05,axiom,
! [VAR_0] : mult(VAR_0,unit) = VAR_0,
file('theBenchmark.p',c05) ).
cnf(c_5,plain,
mult(A,unit) = A,
inference(clausify,[status(thm)],[c05]) ).
fof(c07,axiom,
! [VAR_0,VAR_1,VAR_2] : mult(VAR_0,mult(VAR_1,mult(VAR_0,VAR_2))) = mult(mult(VAR_0,mult(VAR_1,VAR_0)),VAR_2),
file('theBenchmark.p',c07) ).
cnf(c_7,plain,
mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C),
inference(clausify,[status(thm)],[c07]) ).
cnf(c_8,plain,
mult(mult(A,mult(B,A)),C) = mult(A,mult(B,mult(A,C))),
inference(copy,[status(thm)],[c_7]) ).
fof(c08,axiom,
! [VAR_0,VAR_1] : mult(i(VAR_0),mult(VAR_0,VAR_1)) = VAR_1,
file('theBenchmark.p',c08) ).
cnf(c_9,plain,
mult(i(A),mult(A,B)) = B,
inference(clausify,[status(thm)],[c08]) ).
fof(c09,axiom,
! [VAR_0] : mult(op_c,VAR_0) = mult(VAR_0,op_c),
file('theBenchmark.p',c09) ).
cnf(c_10,plain,
mult(op_c,A) = mult(A,op_c),
inference(clausify,[status(thm)],[c09]) ).
fof(goals,axiom,
mult(i(op_c),a) != mult(a,i(op_c)),
file('theBenchmark.p',goals) ).
cnf(c_11,plain,
mult(i(op_c),a) != mult(a,i(op_c)),
inference(clausify,[status(thm)],[goals]) ).
cnf(c_15,plain,
rd(A,unit) = A,
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_25,plain,
mult(i(A),B) = ld(A,B),
inference(paramod,[status(thm)],[c_1,c_9]) ).
cnf(c_274,plain,
rd(A,mult(B,A)) = i(B),
inference(paramod,[status(thm)],[c_9,c_4]) ).
cnf(c_28,plain,
i(A) = rd(B,mult(A,B)),
inference(copy,[status(thm)],[c_274]) ).
cnf(c_29,plain,
mult(i(A),A) = unit,
inference(paramod,[status(thm)],[c_5,c_9]) ).
cnf(c_34,plain,
ld(op_c,mult(A,op_c)) = A,
inference(paramod,[status(thm)],[c_10,c_2]) ).
cnf(c_42,plain,
mult(op_c,mult(A,mult(B,A))) = mult(A,mult(B,mult(A,op_c))),
inference(paramod,[status(thm)],[c_10,c_8]) ).
cnf(c_275,plain,
rd(unit,A) = i(A),
inference(paramod,[status(thm)],[c_29,c_4]) ).
cnf(c_46,plain,
i(A) = rd(unit,A),
inference(copy,[status(thm)],[c_275]) ).
cnf(c_52,plain,
rd(unit,A) = rd(B,mult(A,B)),
inference(paramod,[status(thm)],[c_46,c_28]) ).
cnf(c_55,plain,
mult(rd(unit,A),B) = ld(A,B),
inference(paramod,[status(thm)],[c_46,c_25]) ).
cnf(c_276,plain,
mult(rd(unit,op_c),a) != mult(a,i(op_c)),
inference(paramod,[status(thm)],[c_46,c_11]) ).
cnf(c_56,plain,
mult(rd(unit,op_c),a) != mult(a,rd(unit,op_c)),
inference(paramod,[status(thm)],[c_46,c_276]) ).
cnf(c_277,plain,
ld(op_c,A) = rd(A,op_c),
inference(paramod,[status(thm)],[c_3,c_34]) ).
cnf(c_58,plain,
rd(A,op_c) = ld(op_c,A),
inference(copy,[status(thm)],[c_277]) ).
cnf(c_278,plain,
mult(ld(op_c,unit),a) != mult(a,rd(unit,op_c)),
inference(paramod,[status(thm)],[c_58,c_56]) ).
cnf(c_60,plain,
mult(ld(op_c,unit),a) != mult(a,ld(op_c,unit)),
inference(paramod,[status(thm)],[c_58,c_278]) ).
cnf(c_279,plain,
rd(unit,A) = rd(ld(A,B),B),
inference(paramod,[status(thm)],[c_1,c_52]) ).
cnf(c_79,plain,
rd(ld(A,B),B) = rd(unit,A),
inference(copy,[status(thm)],[c_279]) ).
cnf(c_84,plain,
rd(unit,A) = rd(op_c,mult(op_c,A)),
inference(paramod,[status(thm)],[c_10,c_52]) ).
cnf(c_94,plain,
rd(ld(A,B),B) = rd(op_c,mult(op_c,A)),
inference(paramod,[status(thm)],[c_84,c_79]) ).
cnf(c_96,plain,
mult(rd(op_c,mult(op_c,A)),B) = ld(A,B),
inference(paramod,[status(thm)],[c_84,c_55]) ).
cnf(c_129,plain,
mult(rd(op_c,mult(op_c,A)),A) = unit,
inference(paramod,[status(thm)],[c_84,c_3]) ).
cnf(c_146,plain,
rd(op_c,mult(op_c,A)) = ld(A,unit),
inference(paramod,[status(thm)],[c_94,c_15]) ).
cnf(c_152,plain,
mult(ld(A,unit),A) = unit,
inference(paramod,[status(thm)],[c_146,c_129]) ).
cnf(c_157,plain,
mult(ld(A,unit),B) = ld(A,B),
inference(paramod,[status(thm)],[c_146,c_96]) ).
cnf(c_210,plain,
mult(A,mult(ld(A,unit),B)) = B,
inference(paramod,[status(thm)],[c_157,c_1]) ).
cnf(c_280,plain,
mult(op_c,mult(ld(op_c,unit),mult(A,ld(op_c,unit)))) = mult(ld(op_c,unit),mult(A,unit)),
inference(paramod,[status(thm)],[c_152,c_42]) ).
cnf(c_281,plain,
mult(A,ld(op_c,unit)) = mult(ld(op_c,unit),mult(A,unit)),
inference(paramod,[status(thm)],[c_210,c_280]) ).
cnf(c_282,plain,
mult(A,ld(op_c,unit)) = mult(ld(op_c,unit),A),
inference(paramod,[status(thm)],[c_5,c_281]) ).
cnf(c_272,plain,
mult(ld(op_c,unit),A) = mult(A,ld(op_c,unit)),
inference(copy,[status(thm)],[c_282]) ).
cnf(c_273,plain,
$false,
inference(resolve,[status(thm)],[c_272,c_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP680-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n020.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Fri Sep 25 15:37:19 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 3272254 was started by sandbox2 on n020,
% 0.10/0.38 % Fri Sep 25 15:37:19 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 0.10/0.44
% 0.10/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.44
% 0.10/0.44 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.10/0.44 % Length of proof is 33.
% 0.10/0.44 % Level of proof is 10.
% 0.10/0.44 % Maximum clause weight is 55.000.
% 0.10/0.44 % Given clauses 49.
% 0.10/0.44
% 0.10/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------