%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : FLD030-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.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 01:14:58 PM UTC 2026
% Result : Unsatisfiable 40.30s 5.56s
% Output : Proof 40.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 54 ( 38 unt; 0 def)
% Number of atoms : 82 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 66 ( 38 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-4 aty)
% Number of variables : 66 ( 2 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f30,negated_conjecture,
~ product(d,b,multiply(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_5) ).
fof(f30_nnf,plain,
~ product(d,b,multiply(a,b)),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
~ product(d,b,multiply(a,b)),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c30,plain,
~ product(d,b,multiply(a,b)),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(t159,plain,
ifeq(product(d,b,multiply(a,b)),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c30]) ).
cnf(f19,axiom,
( ~ defined(Y)
| ~ defined(X)
| product(X,Y,multiply(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality_of_multiplication) ).
fof(f19_nnf,plain,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| product(X,Y,multiply(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| product(X,Y,multiply(X,Y)) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( ~ defined(X1)
| ~ defined(X0)
| product(X0,X1,multiply(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi19,axiom,
ifeq(defined(X0),true,ifeq(defined(X1),true,product(X0,X1,multiply(X0,X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(f26,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
fof(f26_nnf,plain,
defined(a),
inference(nnf_transformation,[status(thm)],[f26]) ).
cnf(c26,plain,
defined(a),
inference(cnf_transformation,[status(esa)],[f26_nnf]) ).
cnf(hi25,axiom,
defined(a) = true,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(f27,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
fof(f27_nnf,plain,
defined(b),
inference(nnf_transformation,[status(thm)],[f27]) ).
cnf(c27,plain,
defined(b),
inference(cnf_transformation,[status(esa)],[f27_nnf]) ).
cnf(hi26,axiom,
defined(b) = true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(h71,plain,
product(a,b,multiply(a,b)) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi25,hi26]) ).
cnf(f7,axiom,
( ~ defined(X)
| product(multiplicative_identity,X,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_identity_multiplication) ).
fof(f7_nnf,plain,
! [X] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( ~ defined(X0)
| product(multiplicative_identity,X0,X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,axiom,
ifeq(defined(X0),true,product(multiplicative_identity,X0,X0),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h101,plain,
product(multiplicative_identity,b,b) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi26]) ).
cnf(f9,axiom,
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_multiplication) ).
fof(f9_nnf,plain,
! [Y,X,Z] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [Y,X,Z] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi9,axiom,
ifeq(product(X0,X1,X2),true,product(X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(f29,negated_conjecture,
product(multiplicative_identity,a,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_4) ).
fof(f29_nnf,plain,
product(multiplicative_identity,a,d),
inference(nnf_transformation,[status(thm)],[f29]) ).
cnf(c29,plain,
product(multiplicative_identity,a,d),
inference(cnf_transformation,[status(esa)],[f29_nnf]) ).
cnf(hi28,negated_conjecture,
product(multiplicative_identity,a,d) = true,
inference(equality_encoding,[status(esa)],[c29]) ).
cnf(h155,plain,
product(a,multiplicative_identity,d) = true,
inference(hyper_resolution,[status(thm)],[hi9,hi28]) ).
cnf(f6,axiom,
( ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(U,Z,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_multiplication_2) ).
fof(f6_nnf,plain,
! [U,Z,W,X,Y,V] :
( ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(U,Z,W) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [U,Z,W,X,Y,V] :
( ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(U,Z,W) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( ~ product(X3,X5,X2)
| ~ product(X4,X1,X5)
| ~ product(X3,X4,X0)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X1,X3,X4),true,ifeq(product(X0,X4,X5),true,product(X2,X3,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t109,plain,
product(d,b,multiply(a,b)) = true,
inference(hyper_resolution,[status(thm)],[hi6,h155,h101,h71]) ).
cnf(t412,plain,
product(d,b,multiply(a,b)) = true,
inference(orient,[status(thm)],[t109]) ).
cnf(t3151,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t159,t412]) ).
cnf(t48,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t258,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t48]) ).
cnf(t3152,plain,
false = true,
inference(step,[status(thm)],[t3151,t258]) ).
cnf(t3147,plain,
false = true,
inference(orient,[status(thm)],[t3152]) ).
cnf(f25,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',different_identities) ).
fof(f25_nnf,plain,
~ sum(additive_identity,additive_identity,multiplicative_identity),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
~ sum(additive_identity,additive_identity,multiplicative_identity),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c25,plain,
~ sum(additive_identity,additive_identity,multiplicative_identity),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c25,c30]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t3147]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD030-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.35 % Computer : n008.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Fri Sep 25 10:45:09 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 40.30/5.56 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 40.30/5.56 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------