%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP012+5 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 07:26:10 AM UTC 2026
% Result : Theorem 0.11s 0.59s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 26 ( 12 unt; 0 def)
% Number of atoms : 104 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 115 ( 37 ~; 30 |; 40 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 127 ( 0 sgn 82 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_distribution,conjecture,
! [E] :
( ( ! [X] : product(inverse(X),X,E)
& ! [X] : product(X,inverse(X),E)
& ! [X] : product(E,X,X)
& ! [X] : product(X,E,X)
& ! [X,Y,Z,U,V,W] :
( ( product(X,V,W)
& product(Y,Z,V)
& product(X,Y,U) )
=> product(U,Z,W) )
& ! [X,Y,Z,U,V,W] :
( ( product(U,Z,W)
& product(Y,Z,V)
& product(X,Y,U) )
=> product(X,V,W) )
& ! [X,Y] :
? [Z] : product(X,Y,Z) )
=> ! [U,V,W,X] :
( ( product(V,U,X)
& product(inverse(U),inverse(V),W) )
=> product(inverse(W),inverse(X),E) ) ),
file('theBenchmark.p',prove_distribution) ).
fof(prove_distribution_neg,negated_conjecture,
~ ! [E] :
( ( ! [X] : product(inverse(X),X,E)
& ! [X] : product(X,inverse(X),E)
& ! [X] : product(E,X,X)
& ! [X] : product(X,E,X)
& ! [X,Y,Z,U,V,W] :
( ( product(X,V,W)
& product(Y,Z,V)
& product(X,Y,U) )
=> product(U,Z,W) )
& ! [X,Y,Z,U,V,W] :
( ( product(U,Z,W)
& product(Y,Z,V)
& product(X,Y,U) )
=> product(X,V,W) )
& ! [X,Y] :
? [Z] : product(X,Y,Z) )
=> ! [U,V,W,X] :
( ( product(V,U,X)
& product(inverse(U),inverse(V),W) )
=> product(inverse(W),inverse(X),E) ) ),
inference(assume_negation,[status(cth)],[prove_distribution]) ).
fof(nnf_1,plain,
? [E] :
( ? [U,V,W,X] :
( ~ product(inverse(W),inverse(X),E)
& product(V,U,X)
& product(inverse(U),inverse(V),W) )
& ! [X16] : product(inverse(X16),X16,E)
& ! [X15] : product(X15,inverse(X15),E)
& ! [X14] : product(E,X14,X14)
& ! [X13] : product(X13,E,X13)
& ! [X9,Y,Z,X10,X11,X12] :
( product(X10,Z,X12)
| ~ product(X9,X11,X12)
| ~ product(Y,Z,X11)
| ~ product(X9,Y,X10) )
& ! [X3,X4,X5,X6,X7,X8] :
( product(X3,X7,X8)
| ~ product(X6,X5,X8)
| ~ product(X4,X5,X7)
| ~ product(X3,X4,X6) )
& ! [X0,X1] :
? [X2] : product(X0,X1,X2) ),
inference(fof_nnf,[status(thm)],[prove_distribution_neg]) ).
fof(sk_prove_distribution_neg,plain,
( ~ product(inverse(sK3),inverse(sK4),sK0)
& product(sK2,sK1,sK4)
& product(inverse(sK1),inverse(sK2),sK3)
& ! [X16] : product(inverse(X16),X16,sK0)
& ! [X15] : product(X15,inverse(X15),sK0)
& ! [X14] : product(sK0,X14,X14)
& ! [X13] : product(X13,sK0,X13)
& ! [X9,Y,Z,X10,X11,X12] :
( product(X10,Z,X12)
| ~ product(X9,X11,X12)
| ~ product(Y,Z,X11)
| ~ product(X9,Y,X10) )
& ! [X3,X4,X5,X6,X7,X8] :
( product(X3,X7,X8)
| ~ product(X6,X5,X8)
| ~ product(X4,X5,X7)
| ~ product(X3,X4,X6) )
& ! [X0,X1] : product(X0,X1,sK5(X0,X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK0,sK1,sK2,sK3,sK4]),skolemize(E,sK0),skolemize(X2,sK5(X0,X1)),skolemize(U,sK1),skolemize(V,sK2),skolemize(W,sK3),skolemize(X,sK4)],[nnf_1]) ).
cnf(c_3,negated_conjecture,
( product(A,E,F)
| ~ product(C,D,F)
| ~ product(B,D,E)
| ~ product(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_prove_distribution_neg]) ).
cnf(c_4,negated_conjecture,
( product(C,D,F)
| ~ product(A,E,F)
| ~ product(B,D,E)
| ~ product(A,B,C) ),
inference(split_conjunct,[status(thm)],[sk_prove_distribution_neg]) ).
cnf(c_5,negated_conjecture,
product(A,sK0,A),
inference(split_conjunct,[status(thm)],[sk_prove_distribution_neg]) ).
cnf(c_6,negated_conjecture,
product(sK0,A,A),
inference(split_conjunct,[status(thm)],[sk_prove_distribution_neg]) ).
cnf(c_7,negated_conjecture,
product(A,inverse(A),sK0),
inference(split_conjunct,[status(thm)],[sk_prove_distribution_neg]) ).
cnf(c_8,negated_conjecture,
product(inverse(A),A,sK0),
inference(split_conjunct,[status(thm)],[sk_prove_distribution_neg]) ).
cnf(c_9,negated_conjecture,
product(inverse(sK1),inverse(sK2),sK3),
inference(split_conjunct,[status(thm)],[sk_prove_distribution_neg]) ).
cnf(c_10,negated_conjecture,
product(sK2,sK1,sK4),
inference(split_conjunct,[status(thm)],[sk_prove_distribution_neg]) ).
cnf(c_11,negated_conjecture,
~ product(inverse(sK3),inverse(sK4),sK0),
inference(split_conjunct,[status(thm)],[sk_prove_distribution_neg]) ).
cnf(c_258,negated_conjecture,
( product(inverse(A),C,D)
| ~ product(sK0,B,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_3,c_8]) ).
cnf(c_259,negated_conjecture,
( product(inverse(sK2),sK4,A)
| ~ product(sK0,sK1,A) ),
inference(resolve,[status(thm)],[c_258,c_10]) ).
cnf(c_125,negated_conjecture,
product(inverse(sK2),sK4,sK1),
inference(resolve,[status(thm)],[c_259,c_6]) ).
cnf(c_260,negated_conjecture,
( product(C,inverse(B),D)
| ~ product(A,sK0,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_4,c_7]) ).
cnf(c_261,negated_conjecture,
( product(B,inverse(A),sK0)
| ~ product(sK0,A,B) ),
inference(resolve,[status(thm)],[c_260,c_6]) ).
cnf(c_139,negated_conjecture,
~ product(sK0,sK4,inverse(sK3)),
inference(resolve,[status(thm)],[c_261,c_11]) ).
cnf(c_262,negated_conjecture,
( product(sK0,B,D)
| ~ product(inverse(A),C,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_4,c_8]) ).
cnf(c_263,negated_conjecture,
( product(sK0,B,inverse(A))
| ~ product(A,B,sK0) ),
inference(resolve,[status(thm)],[c_262,c_5]) ).
cnf(c_240,negated_conjecture,
~ product(sK3,sK4,sK0),
inference(resolve,[status(thm)],[c_263,c_139]) ).
cnf(c_264,negated_conjecture,
( product(sK3,A,C)
| ~ product(inverse(sK1),B,C)
| ~ product(inverse(sK2),A,B) ),
inference(resolve,[status(thm)],[c_4,c_9]) ).
cnf(c_265,negated_conjecture,
( product(sK3,A,sK0)
| ~ product(inverse(sK2),A,sK1) ),
inference(resolve,[status(thm)],[c_264,c_8]) ).
cnf(c_256,negated_conjecture,
~ product(inverse(sK2),sK4,sK1),
inference(resolve,[status(thm)],[c_265,c_240]) ).
cnf(c_257,plain,
$false,
inference(resolve,[status(thm)],[c_256,c_125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP012+5 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.55 % Computer : n012.cluster.edu
% 0.08/0.55 % Model : x86_64 x86_64
% 0.08/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.55 % Memory : 8046.5625MB
% 0.08/0.55 % OS : Linux 6.8.0-71-generic
% 0.08/0.56 % CPULimit : 300
% 0.08/0.56 % WCLimit : 300
% 0.08/0.56 % DateTime : Fri Sep 25 14:16:09 UTC 2026
% 0.11/0.56 % CPUTime :
% 0.11/0.56 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.56 % Process 2271085 was started by sandbox on n012,
% 0.11/0.56 % Fri Sep 25 14:16:09 2026
% 0.11/0.56 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.56
% 0.11/0.56 % From the command line: assign(max_seconds, 300).
% 0.11/0.59
% 0.11/0.59 % SZS status Theorem for theBenchmark
% 0.11/0.59
% 0.11/0.59 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.11/0.59 % Length of proof is 15.
% 0.11/0.59 % Level of proof is 5.
% 0.11/0.59 % Maximum clause weight is 16.000.
% 0.11/0.59 % Given clauses 13.
% 0.11/0.59
% 0.11/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------