%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP659-10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 0.69s 0.49s
% Output : CNFRefutation 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 6
% Syntax : Number of formulae : 48 ( 48 unt; 0 def)
% Number of atoms : 48 ( 47 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 : 5 ( 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 : 95 ( 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_2)),VAR_1) = mult(mult(VAR_0,VAR_1),mult(VAR_2,VAR_1)),
file('theBenchmark.p',f05) ).
cnf(c_5,plain,
mult(mult(A,mult(B,C)),B) = mult(mult(A,B),mult(C,B)),
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_8,plain,
rd(A,ld(B,A)) = B,
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_484,plain,
mult(mult(A,B),C) = mult(mult(A,C),mult(ld(C,B),C)),
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_9,plain,
mult(mult(A,B),mult(ld(B,C),B)) = mult(mult(A,C),B),
inference(copy,[status(thm)],[c_484]) ).
cnf(c_17,plain,
ld(mult(A,B),mult(mult(A,C),B)) = mult(ld(B,C),B),
inference(paramod,[status(thm)],[c_9,c_2]) ).
cnf(c_21,plain,
rd(mult(mult(A,B),C),mult(ld(C,B),C)) = mult(A,C),
inference(paramod,[status(thm)],[c_9,c_4]) ).
cnf(c_36,plain,
ld(mult(A,B),mult(C,B)) = mult(ld(B,ld(A,C)),B),
inference(paramod,[status(thm)],[c_1,c_17]) ).
cnf(c_38,plain,
mult(ld(A,A),A) = A,
inference(paramod,[status(thm)],[c_17,c_2]) ).
cnf(c_46,plain,
rd(A,A) = ld(A,A),
inference(paramod,[status(thm)],[c_38,c_4]) ).
cnf(c_53,plain,
rd(mult(A,B),mult(ld(B,C),B)) = mult(rd(A,C),B),
inference(paramod,[status(thm)],[c_3,c_21]) ).
cnf(c_58,plain,
rd(mult(A,B),mult(C,B)) = mult(rd(A,mult(B,C)),B),
inference(paramod,[status(thm)],[c_2,c_53]) ).
cnf(c_485,plain,
mult(rd(A,mult(B,A)),B) = ld(mult(A,B),mult(A,B)),
inference(paramod,[status(thm)],[c_58,c_46]) ).
cnf(c_120,plain,
mult(rd(A,mult(B,A)),B) = mult(ld(B,ld(A,A)),B),
inference(paramod,[status(thm)],[c_36,c_485]) ).
cnf(c_486,plain,
rd(mult(ld(A,ld(B,B)),A),A) = rd(B,mult(A,B)),
inference(paramod,[status(thm)],[c_120,c_4]) ).
cnf(c_487,plain,
ld(A,ld(B,B)) = rd(B,mult(A,B)),
inference(paramod,[status(thm)],[c_4,c_486]) ).
cnf(c_220,plain,
rd(A,mult(B,A)) = ld(B,ld(A,A)),
inference(copy,[status(thm)],[c_487]) ).
cnf(c_488,plain,
mult(rd(A,A),ld(A,A)) = mult(ld(ld(A,A),ld(A,A)),ld(A,A)),
inference(paramod,[status(thm)],[c_38,c_120]) ).
cnf(c_489,plain,
mult(ld(A,A),ld(A,A)) = mult(ld(ld(A,A),ld(A,A)),ld(A,A)),
inference(paramod,[status(thm)],[c_46,c_488]) ).
cnf(c_226,plain,
mult(ld(A,A),ld(A,A)) = ld(A,A),
inference(paramod,[status(thm)],[c_38,c_489]) ).
cnf(c_283,plain,
ld(ld(A,A),ld(A,A)) = ld(A,A),
inference(paramod,[status(thm)],[c_226,c_2]) ).
cnf(c_295,plain,
rd(A,B) = ld(rd(B,A),ld(A,A)),
inference(paramod,[status(thm)],[c_3,c_220]) ).
cnf(c_309,plain,
mult(rd(A,B),rd(B,A)) = ld(B,B),
inference(paramod,[status(thm)],[c_295,c_1]) ).
cnf(c_313,plain,
rd(ld(A,A),rd(A,B)) = rd(B,A),
inference(paramod,[status(thm)],[c_295,c_8]) ).
cnf(c_490,plain,
ld(ld(A,A),mult(B,rd(A,C))) = mult(ld(rd(A,C),ld(rd(C,A),B)),rd(A,C)),
inference(paramod,[status(thm)],[c_309,c_36]) ).
cnf(c_360,plain,
mult(ld(rd(A,B),ld(rd(B,A),C)),rd(A,B)) = ld(ld(A,A),mult(C,rd(A,B))),
inference(copy,[status(thm)],[c_490]) ).
cnf(c_364,plain,
rd(rd(A,B),ld(A,A)) = ld(rd(B,A),ld(rd(A,B),rd(A,B))),
inference(paramod,[status(thm)],[c_309,c_220]) ).
cnf(c_491,plain,
mult(rd(rd(A,B),ld(A,A)),rd(B,A)) = ld(ld(A,A),ld(A,A)),
inference(paramod,[status(thm)],[c_313,c_309]) ).
cnf(c_492,plain,
mult(ld(rd(B,A),ld(rd(A,B),rd(A,B))),rd(B,A)) = ld(ld(A,A),ld(A,A)),
inference(paramod,[status(thm)],[c_364,c_491]) ).
cnf(c_493,plain,
ld(ld(B,B),mult(rd(A,B),rd(B,A))) = ld(ld(A,A),ld(A,A)),
inference(paramod,[status(thm)],[c_360,c_492]) ).
cnf(c_494,plain,
ld(ld(B,B),ld(B,B)) = ld(ld(A,A),ld(A,A)),
inference(paramod,[status(thm)],[c_309,c_493]) ).
cnf(c_495,plain,
ld(B,B) = ld(ld(A,A),ld(A,A)),
inference(paramod,[status(thm)],[c_283,c_494]) ).
cnf(c_375,plain,
ld(A,A) = ld(B,B),
inference(paramod,[status(thm)],[c_283,c_495]) ).
cnf(c_387,plain,
mult(A,ld(B,B)) = A,
inference(paramod,[status(thm)],[c_375,c_1]) ).
cnf(c_390,plain,
mult(ld(A,A),B) = B,
inference(paramod,[status(thm)],[c_375,c_38]) ).
cnf(c_496,plain,
tuple(mult(ld(A,A),x1(ld(A,A))),x1_2(ld(A,A))) != tuple(x1(ld(A,A)),x1_2(ld(A,A))),
inference(paramod,[status(thm)],[c_387,c_6]) ).
cnf(c_497,plain,
tuple(x1(ld(A,A)),x1_2(ld(A,A))) != tuple(x1(ld(A,A)),x1_2(ld(A,A))),
inference(paramod,[status(thm)],[c_390,c_496]) ).
cnf(c_483,plain,
$false,
inference(copy,[status(thm)],[c_497]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP659-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 15:34:26 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 2904373 was started by sandbox on n026,
% 0.10/0.38 % Fri Sep 25 15:34:26 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.69/0.49
% 0.69/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.69/0.49
% 0.69/0.49 % Proof 1 at 0.07 (+ 0.03) seconds.
% 0.69/0.49 % Length of proof is 28.
% 0.69/0.49 % Level of proof is 12.
% 0.69/0.49 % Maximum clause weight is 58.000.
% 0.69/0.49 % Given clauses 39.
% 0.69/0.49
% 0.69/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------