%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP682-10 : 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 : n013.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 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 43 unt; 0 def)
% Number of atoms : 43 ( 42 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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; 3 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f01,axiom,
! [VAR_0] : ld(VAR_0,mult(VAR_0,VAR_0)) = VAR_0,
file('theBenchmark.p',f01) ).
cnf(c_1,plain,
ld(A,mult(A,A)) = A,
inference(clausify,[status(thm)],[f01]) ).
fof(f02,axiom,
! [VAR_0] : rd(mult(VAR_0,VAR_0),VAR_0) = VAR_0,
file('theBenchmark.p',f02) ).
cnf(c_2,plain,
rd(mult(A,A),A) = A,
inference(clausify,[status(thm)],[f02]) ).
fof(f03,axiom,
! [VAR_0,VAR_1] : mult(VAR_0,ld(VAR_0,VAR_1)) = ld(VAR_0,mult(VAR_0,VAR_1)),
file('theBenchmark.p',f03) ).
cnf(c_3,plain,
mult(A,ld(A,B)) = ld(A,mult(A,B)),
inference(clausify,[status(thm)],[f03]) ).
cnf(c_4,plain,
ld(A,mult(A,B)) = mult(A,ld(A,B)),
inference(copy,[status(thm)],[c_3]) ).
fof(f04,axiom,
! [VAR_0,VAR_1] : mult(rd(VAR_0,VAR_1),VAR_1) = rd(mult(VAR_0,VAR_1),VAR_1),
file('theBenchmark.p',f04) ).
cnf(c_5,plain,
mult(rd(A,B),B) = rd(mult(A,B),B),
inference(clausify,[status(thm)],[f04]) ).
cnf(c_6,plain,
rd(mult(A,B),B) = mult(rd(A,B),B),
inference(copy,[status(thm)],[c_5]) ).
fof(f05,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : ld(ld(VAR_0,VAR_1),mult(ld(VAR_0,VAR_1),mult(VAR_2,VAR_3))) = mult(ld(VAR_0,mult(VAR_0,VAR_2)),VAR_3),
file('theBenchmark.p',f05) ).
cnf(c_7,plain,
ld(ld(A,B),mult(ld(A,B),mult(C,D))) = mult(ld(A,mult(A,C)),D),
inference(clausify,[status(thm)],[f05]) ).
cnf(c_101,plain,
mult(ld(A,B),ld(ld(A,B),mult(C,D))) = mult(ld(A,mult(A,C)),D),
inference(paramod,[status(thm)],[c_4,c_7]) ).
cnf(c_8,plain,
mult(ld(A,B),ld(ld(A,B),mult(C,D))) = mult(mult(A,ld(A,C)),D),
inference(paramod,[status(thm)],[c_4,c_101]) ).
fof(f07,axiom,
! [VAR_0,VAR_1] : ld(VAR_0,mult(VAR_0,ld(VAR_1,VAR_1))) = rd(mult(rd(VAR_0,VAR_0),VAR_1),VAR_1),
file('theBenchmark.p',f07) ).
cnf(c_11,plain,
ld(A,mult(A,ld(B,B))) = rd(mult(rd(A,A),B),B),
inference(clausify,[status(thm)],[f07]) ).
cnf(c_102,plain,
mult(A,ld(A,ld(B,B))) = rd(mult(rd(A,A),B),B),
inference(paramod,[status(thm)],[c_4,c_11]) ).
cnf(c_103,plain,
mult(A,ld(A,ld(B,B))) = mult(rd(rd(A,A),B),B),
inference(paramod,[status(thm)],[c_6,c_102]) ).
cnf(c_12,plain,
mult(rd(rd(A,A),B),B) = mult(A,ld(A,ld(B,B))),
inference(copy,[status(thm)],[c_103]) ).
fof(goal,axiom,
ld(ld(x0,x1),mult(ld(x0,x1),x2)) != ld(x0,mult(x0,x2)),
file('theBenchmark.p',goal) ).
cnf(c_13,plain,
ld(ld(x0,x1),mult(ld(x0,x1),x2)) != ld(x0,mult(x0,x2)),
inference(clausify,[status(thm)],[goal]) ).
cnf(c_104,plain,
mult(ld(x0,x1),ld(ld(x0,x1),x2)) != ld(x0,mult(x0,x2)),
inference(paramod,[status(thm)],[c_4,c_13]) ).
cnf(c_14,plain,
mult(ld(x0,x1),ld(ld(x0,x1),x2)) != mult(x0,ld(x0,x2)),
inference(paramod,[status(thm)],[c_4,c_104]) ).
cnf(c_15,plain,
mult(A,ld(A,A)) = A,
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_16,plain,
mult(rd(A,A),A) = A,
inference(paramod,[status(thm)],[c_6,c_2]) ).
cnf(c_105,plain,
mult(mult(A,ld(A,B)),ld(ld(A,mult(A,B)),mult(C,D))) = mult(mult(A,ld(A,C)),D),
inference(paramod,[status(thm)],[c_4,c_8]) ).
cnf(c_18,plain,
mult(mult(A,ld(A,B)),ld(mult(A,ld(A,B)),mult(C,D))) = mult(mult(A,ld(A,C)),D),
inference(paramod,[status(thm)],[c_4,c_105]) ).
cnf(c_106,plain,
ld(A,A) = mult(A,ld(A,ld(A,A))),
inference(paramod,[status(thm)],[c_15,c_4]) ).
cnf(c_33,plain,
mult(A,ld(A,ld(A,A))) = ld(A,A),
inference(copy,[status(thm)],[c_106]) ).
cnf(c_107,plain,
rd(A,A) = mult(rd(rd(A,A),A),A),
inference(paramod,[status(thm)],[c_16,c_6]) ).
cnf(c_108,plain,
rd(A,A) = mult(A,ld(A,ld(A,A))),
inference(paramod,[status(thm)],[c_12,c_107]) ).
cnf(c_38,plain,
rd(A,A) = ld(A,A),
inference(paramod,[status(thm)],[c_33,c_108]) ).
cnf(c_109,plain,
rd(mult(A,A),A) = A,
inference(paramod,[status(thm)],[c_16,c_6]) ).
cnf(c_110,plain,
mult(rd(A,A),A) = A,
inference(paramod,[status(thm)],[c_6,c_109]) ).
cnf(c_39,plain,
mult(ld(A,A),A) = A,
inference(paramod,[status(thm)],[c_38,c_110]) ).
cnf(c_111,plain,
mult(ld(A,B),ld(ld(A,B),C)) = mult(mult(A,ld(A,rd(C,C))),C),
inference(paramod,[status(thm)],[c_16,c_8]) ).
cnf(c_40,plain,
mult(ld(A,B),ld(ld(A,B),C)) = mult(mult(A,ld(A,ld(C,C))),C),
inference(paramod,[status(thm)],[c_38,c_111]) ).
cnf(c_112,plain,
mult(A,ld(mult(A,ld(A,A)),mult(B,C))) = mult(mult(A,ld(A,B)),C),
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_113,plain,
mult(A,ld(A,mult(B,C))) = mult(mult(A,ld(A,B)),C),
inference(paramod,[status(thm)],[c_15,c_112]) ).
cnf(c_81,plain,
mult(mult(A,ld(A,B)),C) = mult(A,ld(A,mult(B,C))),
inference(copy,[status(thm)],[c_113]) ).
cnf(c_114,plain,
mult(ld(A,B),ld(ld(A,B),C)) = mult(A,ld(A,mult(ld(C,C),C))),
inference(paramod,[status(thm)],[c_81,c_40]) ).
cnf(c_99,plain,
mult(ld(A,B),ld(ld(A,B),C)) = mult(A,ld(A,C)),
inference(paramod,[status(thm)],[c_39,c_114]) ).
cnf(c_100,plain,
$false,
inference(resolve,[status(thm)],[c_99,c_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP682-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 15:35:36 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 748341 was started by sandbox on n013,
% 0.10/0.37 % Fri Sep 25 15:35:36 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.39
% 0.14/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.39
% 0.14/0.39 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.14/0.39 % Length of proof is 22.
% 0.14/0.39 % Level of proof is 7.
% 0.14/0.39 % Maximum clause weight is 59.000.
% 0.14/0.39 % Given clauses 16.
% 0.14/0.39
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------