%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG005-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n017.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 02:37:23 PM UTC 2026
% Result : Unsatisfiable 6.18s 1.27s
% Output : Proof 6.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 29 unt; 0 def)
% Number of atoms : 49 ( 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 : 8 ( 8 usr; 6 con; 0-4 aty)
% Number of variables : 45 ( 3 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f26,axiom,
product(additive_identity,X,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity1) ).
fof(f26_nnf,plain,
! [X] : product(additive_identity,X,additive_identity),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [X] : product(additive_identity,X,additive_identity),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c26,plain,
product(additive_identity,X0,additive_identity),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(hi26,axiom,
product(additive_identity,X0,additive_identity) = true,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(h0,plain,
product(additive_identity,b,additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi26]) ).
cnf(f22,axiom,
( sum(V1,V2,V4)
| ~ product(V3,X,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity3) ).
fof(f22_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)],[f22]) ).
fof(f22_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)],[f22_nnf]) ).
cnf(c22,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)],[f22_sk]) ).
cnf(hi22,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)],[c22]) ).
cnf(f29,hypothesis,
product(additive_inverse(a),b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_inverse_times_b) ).
fof(f29_nnf,plain,
product(additive_inverse(a),b,c),
inference(nnf_transformation,[status(thm)],[f29]) ).
cnf(c29,plain,
product(additive_inverse(a),b,c),
inference(cnf_transformation,[status(esa)],[f29_nnf]) ).
cnf(hi29,axiom,
product(additive_inverse(a),b,c) = true,
inference(equality_encoding,[status(esa)],[c29]) ).
cnf(f28,hypothesis,
product(a,b,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).
fof(f28_nnf,plain,
product(a,b,d),
inference(nnf_transformation,[status(thm)],[f28]) ).
cnf(c28,plain,
product(a,b,d),
inference(cnf_transformation,[status(esa)],[f28_nnf]) ).
cnf(hi28,axiom,
product(a,b,d) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(f13,axiom,
sum(additive_inverse(X),X,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f13_nnf,plain,
! [X] : sum(additive_inverse(X),X,additive_identity),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X] : sum(additive_inverse(X),X,additive_identity),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
sum(additive_inverse(X0),X0,additive_identity),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi13,axiom,
sum(additive_inverse(X0),X0,additive_identity) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t5,plain,
sum(c,d,additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi22,hi29,hi28,hi13,h0]) ).
cnf(t334,plain,
sum(c,d,additive_identity) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(f30,negated_conjecture,
~ sum(c,d,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_sum_is_additive_identity) ).
fof(f30_nnf,plain,
~ sum(c,d,additive_identity),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
~ sum(c,d,additive_identity),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c30,plain,
~ sum(c,d,additive_identity),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(goal_0,negated_conjecture,
sum(c,d,additive_identity) != true,
inference(equality_encoding,[status(esa)],[c30]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t334]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG005-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 07:37:02 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.18/1.27 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.18/1.27 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------