%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG010-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 02:37:27 PM UTC 2026
% Result : Unsatisfiable 3.67s 0.99s
% Output : Proof 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 27 unt; 0 def)
% Number of atoms : 27 ( 26 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 18 ( 18 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 39 ( 3 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f18,axiom,
multiply(multiply(Y,X),Y) != multiply(Y,multiply(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',middle_law) ).
fof(f18_nnf,plain,
! [Y,X] : multiply(multiply(Y,X),Y) != multiply(Y,multiply(X,Y)),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [Y,X] : multiply(multiply(Y,X),Y) != multiply(Y,multiply(X,Y)),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
multiply(multiply(X0,X1),X0) != multiply(X0,multiply(X1,X0)),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi19,axiom,
ifeq(multiply(multiply(X0,X1),X0),multiply(X0,multiply(X1,X0)),false,true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(f1,axiom,
multiply(additive_identity,X) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_multiplicative_zero) ).
fof(f1_nnf,plain,
! [X] : multiply(additive_identity,X) = additive_identity,
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] : multiply(additive_identity,X) = additive_identity,
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
multiply(additive_identity,X0) = additive_identity,
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
multiply(additive_identity,X0) = additive_identity,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi19,hi1,hi1]) ).
cnf(t207,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(f19,axiom,
associator(Y,X,Z) != additive_inverse(associator(X,Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associator_skew_symmetry1) ).
fof(f19_nnf,plain,
! [Y,X,Z] : associator(Y,X,Z) != additive_inverse(associator(X,Y,Z)),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [Y,X,Z] : associator(Y,X,Z) != additive_inverse(associator(X,Y,Z)),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
associator(X0,X1,X2) != additive_inverse(associator(X1,X0,X2)),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(f20,axiom,
associator(Z,Y,X) != additive_inverse(associator(X,Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associator_skew_symmetry2) ).
fof(f20_nnf,plain,
! [Z,Y,X] : associator(Z,Y,X) != additive_inverse(associator(X,Y,Z)),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [Z,Y,X] : associator(Z,Y,X) != additive_inverse(associator(X,Y,Z)),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
associator(X0,X1,X2) != additive_inverse(associator(X2,X1,X0)),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(f23,negated_conjecture,
associator(multiply(cx,cx),cy,cz) != add(multiply(associator(cx,cy,cz),cx),multiply(cx,associator(cx,cy,cz))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_skew_symmetry) ).
fof(f23_nnf,plain,
associator(multiply(cx,cx),cy,cz) != add(multiply(associator(cx,cy,cz),cx),multiply(cx,associator(cx,cy,cz))),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
associator(multiply(cx,cx),cy,cz) != add(multiply(associator(cx,cy,cz),cx),multiply(cx,associator(cx,cy,cz))),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
associator(multiply(cx,cx),cy,cz) != add(multiply(associator(cx,cy,cz),cx),multiply(cx,associator(cx,cy,cz))),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c18,c19,c20,c23]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t207]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG010-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n005.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 07:44:02 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.67/0.99 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.67/0.99 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------