%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : FLD030-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.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 01:14:59 PM UTC 2026
% Result : Unsatisfiable 6.81s 1.96s
% Output : Proof 6.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 34 unt; 0 def)
% Number of atoms : 58 ( 16 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 42 ( 26 ~; 16 |; 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; 8 con; 0-4 aty)
% Number of variables : 41 ( 2 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f32,negated_conjecture,
~ product(d,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_7) ).
fof(f32_nnf,plain,
~ product(d,b,c),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
~ product(d,b,c),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c32,plain,
~ product(d,b,c),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(t232,plain,
ifeq(product(d,b,c),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c32]) ).
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(f28,hypothesis,
defined(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_is_defined) ).
fof(f28_nnf,plain,
defined(c),
inference(nnf_transformation,[status(thm)],[f28]) ).
cnf(c28,plain,
defined(c),
inference(cnf_transformation,[status(esa)],[f28_nnf]) ).
cnf(hi27,axiom,
defined(c) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(h117,plain,
product(multiplicative_identity,c,c) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi27]) ).
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(f31,negated_conjecture,
product(multiplicative_identity,a,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_6) ).
fof(f31_nnf,plain,
product(multiplicative_identity,a,d),
inference(nnf_transformation,[status(thm)],[f31]) ).
cnf(c31,plain,
product(multiplicative_identity,a,d),
inference(cnf_transformation,[status(esa)],[f31_nnf]) ).
cnf(hi30,negated_conjecture,
product(multiplicative_identity,a,d) = true,
inference(equality_encoding,[status(esa)],[c31]) ).
cnf(f30,negated_conjecture,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_5) ).
fof(f30_nnf,plain,
product(a,b,c),
inference(nnf_transformation,[status(thm)],[f30]) ).
cnf(c30,plain,
product(a,b,c),
inference(cnf_transformation,[status(esa)],[f30_nnf]) ).
cnf(hi29,negated_conjecture,
product(a,b,c) = true,
inference(equality_encoding,[status(esa)],[c30]) ).
cnf(t52,plain,
product(d,b,c) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi30,hi29,h117]) ).
cnf(t446,plain,
product(d,b,c) = true,
inference(orient,[status(thm)],[t52]) ).
cnf(t3856,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t232,t446]) ).
cnf(t79,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t79]) ).
cnf(t3857,plain,
false = true,
inference(step,[status(thm)],[t3856,t256]) ).
cnf(t3852,plain,
false = true,
inference(orient,[status(thm)],[t3857]) ).
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,c32]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t3852]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD030-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n016.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 : Fri Sep 25 10:48:58 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.81/1.96 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.81/1.96 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------