%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP658-10 : 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 : n002.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 07:31:05 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.46s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 35 unt; 0 def)
% Number of atoms : 35 ( 34 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 0 con; 1-2 aty)
% Number of variables : 78 ( 0 sgn 12 !; 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(f04,axiom,
! [VAR_0,VAR_1] : rd(mult(VAR_0,VAR_1),VAR_1) = VAR_0,
file('theBenchmark.p',f04) ).
cnf(c_4,plain,
rd(mult(A,B),B) = A,
inference(clausify,[status(thm)],[f04]) ).
fof(f05,axiom,
! [VAR_0,VAR_1,VAR_2] : mult(mult(VAR_0,mult(VAR_1,VAR_1)),VAR_2) = mult(mult(VAR_0,VAR_1),mult(VAR_1,VAR_2)),
file('theBenchmark.p',f05) ).
cnf(c_5,plain,
mult(mult(A,mult(B,B)),C) = mult(mult(A,B),mult(B,C)),
inference(clausify,[status(thm)],[f05]) ).
fof(goal,axiom,
! [VAR_0] : tuple(mult(VAR_0,x1(VAR_0)),mult(x1_2(VAR_0),VAR_0)) != tuple(x1(VAR_0),x1_2(VAR_0)),
file('theBenchmark.p',goal) ).
cnf(c_6,plain,
tuple(mult(A,x1(A)),mult(x1_2(A),A)) != tuple(x1(A),x1_2(A)),
inference(clausify,[status(thm)],[goal]) ).
cnf(c_7,plain,
ld(rd(A,B),A) = B,
inference(paramod,[status(thm)],[c_3,c_2]) ).
cnf(c_8,plain,
rd(A,ld(B,A)) = B,
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_9,plain,
mult(mult(A,B),mult(B,ld(mult(A,mult(B,B)),C))) = C,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_85,plain,
ld(mult(A,B),C) = mult(B,ld(mult(A,mult(B,B)),C)),
inference(paramod,[status(thm)],[c_9,c_2]) ).
cnf(c_15,plain,
mult(A,ld(mult(B,mult(A,A)),C)) = ld(mult(B,A),C),
inference(copy,[status(thm)],[c_85]) ).
cnf(c_86,plain,
mult(A,ld(B,C)) = ld(mult(rd(B,mult(A,A)),A),C),
inference(paramod,[status(thm)],[c_3,c_15]) ).
cnf(c_18,plain,
ld(mult(rd(A,mult(B,B)),B),C) = mult(B,ld(A,C)),
inference(copy,[status(thm)],[c_86]) ).
cnf(c_21,plain,
rd(A,mult(B,ld(C,A))) = mult(rd(C,mult(B,B)),B),
inference(paramod,[status(thm)],[c_18,c_8]) ).
cnf(c_22,plain,
rd(A,A) = mult(rd(B,mult(B,B)),B),
inference(paramod,[status(thm)],[c_1,c_21]) ).
cnf(c_87,plain,
rd(A,mult(B,C)) = mult(rd(rd(A,C),mult(B,B)),B),
inference(paramod,[status(thm)],[c_7,c_21]) ).
cnf(c_30,plain,
mult(rd(rd(A,B),mult(C,C)),C) = rd(A,mult(C,B)),
inference(copy,[status(thm)],[c_87]) ).
cnf(c_37,plain,
ld(rd(A,mult(A,A)),rd(B,B)) = A,
inference(paramod,[status(thm)],[c_22,c_2]) ).
cnf(c_88,plain,
ld(rd(A,A),B) = mult(C,ld(C,B)),
inference(paramod,[status(thm)],[c_22,c_18]) ).
cnf(c_45,plain,
ld(rd(A,A),B) = B,
inference(paramod,[status(thm)],[c_1,c_88]) ).
cnf(c_89,plain,
rd(A,mult(B,ld(B,A))) = rd(C,C),
inference(paramod,[status(thm)],[c_22,c_21]) ).
cnf(c_47,plain,
rd(A,A) = rd(B,B),
inference(paramod,[status(thm)],[c_1,c_89]) ).
cnf(c_49,plain,
mult(rd(A,A),B) = B,
inference(paramod,[status(thm)],[c_47,c_3]) ).
cnf(c_90,plain,
ld(mult(rd(rd(A,A),mult(B,B)),B),C) = mult(B,C),
inference(paramod,[status(thm)],[c_45,c_18]) ).
cnf(c_51,plain,
ld(rd(A,mult(B,A)),C) = mult(B,C),
inference(paramod,[status(thm)],[c_30,c_90]) ).
cnf(c_53,plain,
mult(A,rd(B,B)) = A,
inference(paramod,[status(thm)],[c_51,c_37]) ).
cnf(c_91,plain,
tuple(x1(rd(A,A)),mult(x1_2(rd(A,A)),rd(A,A))) != tuple(x1(rd(A,A)),x1_2(rd(A,A))),
inference(paramod,[status(thm)],[c_49,c_6]) ).
cnf(c_92,plain,
tuple(x1(rd(A,A)),x1_2(rd(A,A))) != tuple(x1(rd(A,A)),x1_2(rd(A,A))),
inference(paramod,[status(thm)],[c_53,c_91]) ).
cnf(c_84,plain,
$false,
inference(copy,[status(thm)],[c_92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP658-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n002.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Fri Sep 25 15:34:04 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.42 % Process 3660300 was started by sandbox2 on n002,
% 0.16/0.42 % Fri Sep 25 15:34:04 2026
% 0.16/0.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.43
% 0.16/0.43 % From the command line: assign(max_seconds, 300).
% 0.16/0.46
% 0.16/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.46
% 0.16/0.46 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.16/0.46 % Length of proof is 21.
% 0.16/0.46 % Level of proof is 9.
% 0.16/0.46 % Maximum clause weight is 60.000.
% 0.16/0.46 % Given clauses 19.
% 0.16/0.46
% 0.16/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------