%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG040-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/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 02:37:34 PM UTC 2026
% Result : Unsatisfiable 6.61s 1.35s
% Output : Proof 6.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 27 unt; 0 def)
% Number of atoms : 47 ( 10 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 38 ( 22 ~; 16 |; 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 : 35 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f23,negated_conjecture,
product(d,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_plus_a) ).
fof(f23_nnf,plain,
product(d,a,additive_identity),
inference(nnf_transformation,[status(thm)],[f23]) ).
cnf(c23,plain,
product(d,a,additive_identity),
inference(cnf_transformation,[status(esa)],[f23_nnf]) ).
cnf(hi23,negated_conjecture,
product(d,a,additive_identity) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(h0,plain,
product(d,a,additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi23]) ).
cnf(f13,axiom,
( sum(V1,V2,V4)
| ~ product(V3,X,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity3) ).
fof(f13_nnf,plain,
! [Y,X,V1,Z,V2,V3,V4] :
( sum(V1,V2,V4)
| ~ product(V3,X,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [Y,X,V1,Z,V2,V3,V4] :
( sum(V1,V2,V4)
| ~ product(V3,X,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( sum(X2,X4,X6)
| ~ product(X5,X1,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi13,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X3,X1,X4),true,ifeq(sum(X0,X3,X5),true,ifeq(product(X5,X1,X6),true,sum(X2,X4,X6),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(f24,negated_conjecture,
product(b,a,l),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_plus_a) ).
fof(f24_nnf,plain,
product(b,a,l),
inference(nnf_transformation,[status(thm)],[f24]) ).
cnf(c24,plain,
product(b,a,l),
inference(cnf_transformation,[status(esa)],[f24_nnf]) ).
cnf(hi24,negated_conjecture,
product(b,a,l) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(f25,negated_conjecture,
product(c,a,n),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_plus_a) ).
fof(f25_nnf,plain,
product(c,a,n),
inference(nnf_transformation,[status(thm)],[f25]) ).
cnf(c25,plain,
product(c,a,n),
inference(cnf_transformation,[status(esa)],[f25_nnf]) ).
cnf(hi25,negated_conjecture,
product(c,a,n) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(f22,negated_conjecture,
sum(b,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_plus_c) ).
fof(f22_nnf,plain,
sum(b,c,d),
inference(nnf_transformation,[status(thm)],[f22]) ).
cnf(c22,plain,
sum(b,c,d),
inference(cnf_transformation,[status(esa)],[f22_nnf]) ).
cnf(hi22,negated_conjecture,
sum(b,c,d) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t14,plain,
sum(l,n,additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi24,hi25,hi22,h0]) ).
cnf(t297,plain,
sum(l,n,additive_identity) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(f26,negated_conjecture,
~ sum(l,n,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
fof(f26_nnf,plain,
~ sum(l,n,additive_identity),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
~ sum(l,n,additive_identity),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c26,plain,
~ sum(l,n,additive_identity),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(goal_0,negated_conjecture,
sum(l,n,additive_identity) != true,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t297]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG040-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 07:55:58 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.61/1.35 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.61/1.35 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------