%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG040-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 02:37:34 PM UTC 2026
% Result : Unsatisfiable 4.00s 0.96s
% Output : Proof 4.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 30 unt; 0 def)
% Number of atoms : 58 ( 13 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 46 ( 26 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-4 aty)
% Number of variables : 50 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f19,hypothesis,
( product(B,A,C)
| ~ product(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_symmetry) ).
fof(f19_nnf,plain,
! [A,B,C] :
( product(B,A,C)
| ~ product(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [A,B,C] :
( product(B,A,C)
| ~ product(A,B,C) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi19,axiom,
ifeq(product(X0,X1,X2),true,product(X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(f21,negated_conjecture,
product(d,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_plus_a) ).
fof(f21_nnf,plain,
product(d,a,additive_identity),
inference(nnf_transformation,[status(thm)],[f21]) ).
cnf(c21,plain,
product(d,a,additive_identity),
inference(cnf_transformation,[status(esa)],[f21_nnf]) ).
cnf(hi21,negated_conjecture,
product(d,a,additive_identity) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(h1,plain,
product(a,d,additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi21]) ).
cnf(f23,negated_conjecture,
product(c,a,n),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_plus_a) ).
fof(f23_nnf,plain,
product(c,a,n),
inference(nnf_transformation,[status(thm)],[f23]) ).
cnf(c23,plain,
product(c,a,n),
inference(cnf_transformation,[status(esa)],[f23_nnf]) ).
cnf(hi23,negated_conjecture,
product(c,a,n) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(h3,plain,
product(a,c,n) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi23]) ).
cnf(f22,negated_conjecture,
product(b,a,l),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_plus_a) ).
fof(f22_nnf,plain,
product(b,a,l),
inference(nnf_transformation,[status(thm)],[f22]) ).
cnf(c22,plain,
product(b,a,l),
inference(cnf_transformation,[status(esa)],[f22_nnf]) ).
cnf(hi22,negated_conjecture,
product(b,a,l) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(h2,plain,
product(a,b,l) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi22]) ).
cnf(f11,axiom,
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
fof(f11_nnf,plain,
! [X,Y,V1,Z,V2,V3,V4] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Y,V1,Z,V2,V3,V4] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( sum(X2,X4,X6)
| ~ product(X0,X5,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi11,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(sum(X1,X3,X5),true,ifeq(product(X0,X5,X6),true,sum(X2,X4,X6),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(f20,negated_conjecture,
sum(b,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_plus_c) ).
fof(f20_nnf,plain,
sum(b,c,d),
inference(nnf_transformation,[status(thm)],[f20]) ).
cnf(c20,plain,
sum(b,c,d),
inference(cnf_transformation,[status(esa)],[f20_nnf]) ).
cnf(hi20,negated_conjecture,
sum(b,c,d) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t18,plain,
sum(l,n,additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi11,h2,h3,hi20,h1]) ).
cnf(t318,plain,
sum(l,n,additive_identity) = true,
inference(orient,[status(thm)],[t18]) ).
cnf(f24,negated_conjecture,
~ sum(l,n,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
fof(f24_nnf,plain,
~ sum(l,n,additive_identity),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
~ sum(l,n,additive_identity),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
~ sum(l,n,additive_identity),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(goal_0,negated_conjecture,
sum(l,n,additive_identity) != true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t318]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG040-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n026.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 07:58:38 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.00/0.96 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.00/0.96 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------