%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG004-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.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 54.01s 7.26s
% Output : Proof 54.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 72 ( 56 unt; 0 def)
% Number of atoms : 124 ( 21 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 110 ( 58 ~; 52 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-4 aty)
% Number of variables : 155 ( 6 sgn 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f23,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(f23_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)],[f23]) ).
fof(f23_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)],[f23_nnf]) ).
cnf(c23,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)],[f23_sk]) ).
cnf(hi23,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)],[c23]) ).
cnf(f14,axiom,
product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
fof(f14_nnf,plain,
! [X,Y] : product(X,Y,multiply(X,Y)),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X,Y] : product(X,Y,multiply(X,Y)),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi14,axiom,
product(X0,X1,multiply(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(f30,axiom,
product(X,additive_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity2) ).
fof(f30_nnf,plain,
! [X] : product(X,additive_identity,additive_identity),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [X] : product(X,additive_identity,additive_identity),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c30,plain,
product(X0,additive_identity,additive_identity),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(hi30,axiom,
product(X0,additive_identity,additive_identity) = true,
inference(equality_encoding,[status(esa)],[c30]) ).
cnf(f13,axiom,
sum(X,additive_identity,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
fof(f13_nnf,plain,
! [X] : sum(X,additive_identity,X),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X] : sum(X,additive_identity,X),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
sum(X0,additive_identity,X0),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi13,axiom,
sum(X0,additive_identity,X0) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(f32,hypothesis,
product(additive_inverse(a),additive_inverse(b),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_inverse_times_b_inverse) ).
fof(f32_nnf,plain,
product(additive_inverse(a),additive_inverse(b),d),
inference(nnf_transformation,[status(thm)],[f32]) ).
cnf(c32,plain,
product(additive_inverse(a),additive_inverse(b),d),
inference(cnf_transformation,[status(esa)],[f32_nnf]) ).
cnf(hi32,axiom,
product(additive_inverse(a),additive_inverse(b),d) = true,
inference(equality_encoding,[status(esa)],[c32]) ).
cnf(h13,plain,
sum(multiply(additive_inverse(a),additive_inverse(b)),additive_identity,d) = true,
inference(hyper_resolution,[status(thm)],[hi23,hi14,hi30,hi13,hi32]) ).
cnf(f29,axiom,
product(additive_identity,X,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity1) ).
fof(f29_nnf,plain,
! [X] : product(additive_identity,X,additive_identity),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [X] : product(additive_identity,X,additive_identity),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c29,plain,
product(additive_identity,X0,additive_identity),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(hi29,axiom,
product(additive_identity,X0,additive_identity) = true,
inference(equality_encoding,[status(esa)],[c29]) ).
cnf(h10,plain,
product(additive_identity,b,additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi29]) ).
cnf(f25,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(f25_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)],[f25]) ).
fof(f25_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)],[f25_nnf]) ).
cnf(c25,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)],[f25_sk]) ).
cnf(hi25,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)],[c25]) ).
cnf(f31,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b) ).
fof(f31_nnf,plain,
product(a,b,c),
inference(nnf_transformation,[status(thm)],[f31]) ).
cnf(c31,plain,
product(a,b,c),
inference(cnf_transformation,[status(esa)],[f31_nnf]) ).
cnf(hi31,axiom,
product(a,b,c) = true,
inference(equality_encoding,[status(esa)],[c31]) ).
cnf(f16,axiom,
sum(additive_inverse(X),X,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f16_nnf,plain,
! [X] : sum(additive_inverse(X),X,additive_identity),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X] : sum(additive_inverse(X),X,additive_identity),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
sum(additive_inverse(X0),X0,additive_identity),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi16,axiom,
sum(additive_inverse(X0),X0,additive_identity) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(h12,plain,
sum(multiply(additive_inverse(a),b),c,additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi25,hi14,hi31,hi16,h10]) ).
cnf(h11,plain,
sum(multiply(additive_inverse(a),additive_inverse(b)),multiply(additive_inverse(a),b),additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi23,hi14,hi14,hi16,hi30]) ).
cnf(f19,axiom,
( sum(U,Z,W)
| ~ sum(X,V,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition2) ).
fof(f19_nnf,plain,
! [X,Y,U,Z,V,W] :
( sum(U,Z,W)
| ~ sum(X,V,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X,Y,U,Z,V,W] :
( sum(U,Z,W)
| ~ sum(X,V,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( sum(X2,X3,X5)
| ~ sum(X0,X4,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi19,axiom,
ifeq(sum(X0,X1,X2),true,ifeq(sum(X1,X3,X4),true,ifeq(sum(X0,X4,X5),true,sum(X2,X3,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(h14,plain,
sum(additive_identity,c,d) = true,
inference(hyper_resolution,[status(thm)],[hi19,h11,h12,h13]) ).
cnf(f27,axiom,
( equalish(U,V)
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_is_well_defined) ).
fof(f27_nnf,plain,
! [X,Y,U,V] :
( equalish(U,V)
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [X,Y,U,V] :
( equalish(U,V)
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c27,plain,
( equalish(X2,X3)
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(hi27,axiom,
ifeq(sum(X0,X1,X2),true,ifeq(sum(X0,X1,X3),true,equalish(X2,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(f12,axiom,
sum(additive_identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).
fof(f12_nnf,plain,
! [X] : sum(additive_identity,X,X),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X] : sum(additive_identity,X,X),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi12,axiom,
sum(additive_identity,X0,X0) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t1,plain,
equalish(c,d) = true,
inference(hyper_resolution,[status(thm)],[hi27,hi12,h14]) ).
cnf(t352,plain,
equalish(c,d) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(f33,negated_conjecture,
~ equalish(c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_equals_d) ).
fof(f33_nnf,plain,
~ equalish(c,d),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
~ equalish(c,d),
inference(skolemisation,[status(esa)],[f33_nnf]) ).
cnf(c33,plain,
~ equalish(c,d),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
cnf(goal_0,negated_conjecture,
equalish(c,d) != true,
inference(equality_encoding,[status(esa)],[c33]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t352]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG004-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n015.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 : Thu Sep 24 07:44:41 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 54.01/7.26 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 54.01/7.26 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------