%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP756-1 : 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 : n016.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 07:31:23 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.50s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 6
% 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 : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 118 ( 0 sgn 11 !; 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(VAR_0,mult(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(A,mult(mult(B,B),C)) = mult(mult(A,B),mult(B,C)),
inference(clausify,[status(thm)],[f05]) ).
cnf(c_6,plain,
mult(mult(A,B),mult(B,C)) = mult(A,mult(mult(B,B),C)),
inference(copy,[status(thm)],[c_5]) ).
fof(goals,axiom,
mult(mult(a,b),c) != mult(a,mult(b,c)),
file('theBenchmark.p',goals) ).
cnf(c_7,plain,
mult(mult(a,b),c) != mult(a,mult(b,c)),
inference(clausify,[status(thm)],[goals]) ).
cnf(c_8,plain,
ld(rd(A,B),A) = B,
inference(paramod,[status(thm)],[c_3,c_2]) ).
cnf(c_9,plain,
rd(A,ld(B,A)) = B,
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_10,plain,
mult(mult(A,B),C) = mult(A,mult(mult(B,B),ld(B,C))),
inference(paramod,[status(thm)],[c_1,c_6]) ).
cnf(c_11,plain,
mult(mult(A,B),mult(B,ld(mult(B,B),C))) = mult(A,C),
inference(paramod,[status(thm)],[c_1,c_6]) ).
cnf(c_12,plain,
ld(mult(A,B),mult(A,mult(mult(B,B),C))) = mult(B,C),
inference(paramod,[status(thm)],[c_6,c_2]) ).
cnf(c_155,plain,
ld(A,mult(mult(A,B),C)) = mult(mult(B,B),ld(B,C)),
inference(paramod,[status(thm)],[c_10,c_2]) ).
cnf(c_17,plain,
mult(mult(A,A),ld(A,B)) = ld(C,mult(mult(C,A),B)),
inference(copy,[status(thm)],[c_155]) ).
cnf(c_20,plain,
mult(a,mult(mult(b,b),ld(b,c))) != mult(a,mult(b,c)),
inference(paramod,[status(thm)],[c_10,c_7]) ).
cnf(c_156,plain,
mult(mult(A,A),ld(A,B)) = ld(rd(C,A),mult(C,B)),
inference(paramod,[status(thm)],[c_3,c_17]) ).
cnf(c_23,plain,
ld(rd(A,B),mult(A,C)) = mult(mult(B,B),ld(B,C)),
inference(copy,[status(thm)],[c_156]) ).
cnf(c_27,plain,
ld(rd(A,B),C) = mult(mult(B,B),ld(B,ld(A,C))),
inference(paramod,[status(thm)],[c_1,c_23]) ).
cnf(c_29,plain,
mult(mult(A,A),ld(A,ld(B,B))) = A,
inference(paramod,[status(thm)],[c_27,c_8]) ).
cnf(c_30,plain,
ld(mult(A,A),A) = ld(A,ld(B,B)),
inference(paramod,[status(thm)],[c_29,c_2]) ).
cnf(c_33,plain,
mult(A,ld(mult(A,A),A)) = ld(B,B),
inference(paramod,[status(thm)],[c_30,c_1]) ).
cnf(c_34,plain,
rd(ld(A,A),ld(mult(B,B),B)) = B,
inference(paramod,[status(thm)],[c_30,c_9]) ).
cnf(c_157,plain,
ld(mult(A,B),mult(A,C)) = mult(B,ld(mult(B,B),C)),
inference(paramod,[status(thm)],[c_11,c_2]) ).
cnf(c_36,plain,
mult(A,ld(mult(A,A),B)) = ld(mult(C,A),mult(C,B)),
inference(copy,[status(thm)],[c_157]) ).
cnf(c_158,plain,
ld(mult(A,B),mult(A,B)) = mult(B,ld(B,ld(C,C))),
inference(paramod,[status(thm)],[c_29,c_12]) ).
cnf(c_41,plain,
ld(mult(A,B),mult(A,B)) = ld(C,C),
inference(paramod,[status(thm)],[c_1,c_158]) ).
cnf(c_42,plain,
mult(a,ld(A,mult(mult(A,b),c))) != mult(a,mult(b,c)),
inference(paramod,[status(thm)],[c_17,c_20]) ).
cnf(c_159,plain,
ld(A,mult(B,ld(B,A))) = ld(C,C),
inference(paramod,[status(thm)],[c_1,c_41]) ).
cnf(c_44,plain,
ld(A,A) = ld(B,B),
inference(paramod,[status(thm)],[c_1,c_159]) ).
cnf(c_50,plain,
mult(A,ld(B,B)) = A,
inference(paramod,[status(thm)],[c_44,c_1]) ).
cnf(c_160,plain,
ld(mult(A,B),mult(A,mult(mult(B,B),ld(mult(B,B),C)))) = ld(mult(D,B),mult(D,C)),
inference(paramod,[status(thm)],[c_36,c_12]) ).
cnf(c_113,plain,
ld(mult(A,B),mult(A,C)) = ld(mult(D,B),mult(D,C)),
inference(paramod,[status(thm)],[c_1,c_160]) ).
cnf(c_161,plain,
ld(mult(A,B),A) = ld(mult(C,B),mult(C,ld(D,D))),
inference(paramod,[status(thm)],[c_50,c_113]) ).
cnf(c_122,plain,
ld(mult(A,B),A) = ld(mult(C,B),C),
inference(paramod,[status(thm)],[c_50,c_161]) ).
cnf(c_162,plain,
ld(A,B) = ld(mult(C,ld(B,A)),C),
inference(paramod,[status(thm)],[c_1,c_122]) ).
cnf(c_135,plain,
ld(mult(A,ld(B,C)),A) = ld(C,B),
inference(copy,[status(thm)],[c_162]) ).
cnf(c_137,plain,
rd(A,ld(mult(B,C),B)) = mult(A,C),
inference(paramod,[status(thm)],[c_122,c_9]) ).
cnf(c_163,plain,
ld(ld(A,A),B) = ld(mult(C,ld(mult(B,B),B)),C),
inference(paramod,[status(thm)],[c_33,c_122]) ).
cnf(c_164,plain,
ld(ld(A,A),B) = ld(B,mult(B,B)),
inference(paramod,[status(thm)],[c_135,c_163]) ).
cnf(c_142,plain,
ld(ld(A,A),B) = B,
inference(paramod,[status(thm)],[c_2,c_164]) ).
cnf(c_165,plain,
rd(ld(A,A),ld(mult(B,C),B)) = C,
inference(paramod,[status(thm)],[c_122,c_34]) ).
cnf(c_143,plain,
mult(ld(A,A),B) = B,
inference(paramod,[status(thm)],[c_137,c_165]) ).
cnf(c_166,plain,
mult(a,ld(ld(A,A),mult(b,c))) != mult(a,mult(b,c)),
inference(paramod,[status(thm)],[c_143,c_42]) ).
cnf(c_167,plain,
mult(a,mult(b,c)) != mult(a,mult(b,c)),
inference(paramod,[status(thm)],[c_142,c_166]) ).
cnf(c_154,plain,
$false,
inference(copy,[status(thm)],[c_167]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP756-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n016.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Fri Sep 25 15:49:14 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 2785588 was started by sandbox2 on n016,
% 0.17/0.44 % Fri Sep 25 15:49:14 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 0.17/0.50
% 0.17/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.50
% 0.17/0.50 % Proof 1 at 0.03 (+ 0.02) seconds.
% 0.17/0.50 % Length of proof is 32.
% 0.17/0.50 % Level of proof is 13.
% 0.17/0.50 % Maximum clause weight is 31.000.
% 0.17/0.50 % Given clauses 47.
% 0.17/0.50
% 0.17/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------