%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP711+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n009.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 : Fri Sep 25 01:28:16 PM UTC 2026
% Result : Theorem 7.88s 1.62s
% Output : Proof 7.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 22 unt; 0 def)
% Number of atoms : 56 ( 55 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 30 ( 9 ~; 11 |; 6 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 24 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A] : mult(i(A),A) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
fof(f4_nnf,plain,
! [A] : mult(i(A),A) = unit,
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A] : mult(i(A),A) = unit,
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
mult(i(X0),X0) = unit,
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f3,axiom,
! [A] : mult(A,i(A)) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
fof(f3_nnf,plain,
! [A] : mult(A,i(A)) = unit,
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A] : mult(A,i(A)) = unit,
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
mult(X0,i(X0)) = unit,
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f2,axiom,
! [C,B,A] : mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
fof(f2_nnf,plain,
! [C,B,A] : mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B,C] : mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
mult(X2,mult(X1,mult(X1,X0))) = mult(mult(mult(X2,X1),X1),X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f0,axiom,
! [A] : mult(A,unit) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
fof(f0_nnf,plain,
! [A] : mult(A,unit) = A,
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A] : mult(A,unit) = A,
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
mult(X0,unit) = X0,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p14,plain,
mult(X0,mult(X1,X1)) = mult(mult(X0,X1),X1),
inference(superposition,[status(thm)],[c2,c0]) ).
cnf(p63,plain,
mult(X0,mult(i(X0),i(X0))) = i(X0),
inference(superposition,[status(thm)],[c3,p14]) ).
fof(f5,conjecture,
! [X6,X7,X8] :
( ( mult(X7,X6) = mult(X8,X6)
=> X7 = X8 )
& ( mult(X6,X7) = mult(X6,X8)
=> X7 = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f5_neg,negated_conjecture,
~ ! [X6,X7,X8] :
( ( mult(X7,X6) = mult(X8,X6)
=> X7 = X8 )
& ( mult(X6,X7) = mult(X6,X8)
=> X7 = X8 ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f5_nnf,plain,
? [X6,X7,X8] :
( ( X7 != X8
& mult(X7,X6) = mult(X8,X6) )
| ( X7 != X8
& mult(X6,X7) = mult(X6,X8) ) ),
inference(nnf_transformation,[status(thm)],[f5_neg]) ).
fof(f5_sk,plain,
( ( sk1 != sk2
& mult(sk1,sk0) = mult(sk2,sk0) )
| ( sk1 != sk2
& mult(sk0,sk1) = mult(sk0,sk2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f5_nnf]) ).
cnf(c5,plain,
( mult(sk1,sk0) = mult(sk2,sk0)
| mult(sk0,sk1) = mult(sk0,sk2) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p13,plain,
( mult(sk2,mult(sk0,mult(sk0,X0))) = mult(mult(mult(sk1,sk0),sk0),X0)
| mult(sk0,sk1) = mult(sk0,sk2) ),
inference(superposition,[status(thm)],[c5,c2]) ).
cnf(p49,plain,
( mult(sk1,mult(sk0,mult(sk0,X0))) = mult(sk2,mult(sk0,mult(sk0,X0)))
| mult(sk0,sk1) = mult(sk0,sk2) ),
inference(superposition,[status(thm)],[p13,c2]) ).
cnf(p870,plain,
( sk1 = sk2
| mult(sk0,sk1) = mult(sk0,sk2) ),
inference(superposition,[status(thm)],[p63,p49]) ).
cnf(p69,plain,
mult(X0,mult(X1,mult(X1,X2))) = mult(mult(X0,mult(X1,X1)),X2),
inference(superposition,[status(thm)],[p14,c2]) ).
cnf(p981,plain,
( mult(X0,mult(sk0,mult(sk0,sk1))) = mult(mult(X0,mult(sk0,sk0)),sk2)
| sk1 = sk2 ),
inference(superposition,[status(thm)],[p870,p69]) ).
cnf(p991,plain,
( mult(i(mult(sk0,sk0)),mult(sk0,mult(sk0,sk1))) = sk2
| sk1 = sk2 ),
inference(superposition,[status(thm)],[c4,p981]) ).
cnf(p1004,plain,
( sk2 = sk1
| sk1 = sk2 ),
inference(superposition,[status(thm)],[p991,p69]) ).
cnf(c8,plain,
( sk1 != sk2
| sk1 != sk2 ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p9,plain,
sk1 != sk2,
inference(factoring,[status(thm)],[c8]) ).
cnf(p1075,plain,
( sk1 != sk1
| sk1 = sk2 ),
inference(superposition,[status(thm)],[p1004,p9]) ).
cnf(p1076,plain,
sk1 = sk2,
inference(equality_resolution,[status(thm)],[p1075]) ).
cnf(p1077,plain,
$false,
inference(resolution,[status(thm)],[p1076,p9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP711+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 15:48:13 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.88/1.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.88/1.62 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------