%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : FLD025-4 : 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 01:14:57 PM UTC 2026
% Result : Unsatisfiable 14.85s 2.33s
% Output : Proof 14.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 64 ( 48 unt; 0 def)
% Number of atoms : 96 ( 24 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 74 ( 42 ~; 32 |; 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 : 10 ( 10 usr; 9 con; 0-4 aty)
% Number of variables : 86 ( 2 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f34,negated_conjecture,
~ product(d,b,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_9) ).
fof(f34_nnf,plain,
~ product(d,b,u),
inference(nnf_transformation,[status(thm)],[f34]) ).
fof(f34_sk,plain,
~ product(d,b,u),
inference(skolemisation,[status(esa)],[f34_nnf]) ).
cnf(c34,plain,
~ product(d,b,u),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(t232,plain,
ifeq(product(d,b,u),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c34]) ).
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(f33,negated_conjecture,
product(a,c,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_8) ).
fof(f33_nnf,plain,
product(a,c,u),
inference(nnf_transformation,[status(thm)],[f33]) ).
cnf(c33,plain,
product(a,c,u),
inference(cnf_transformation,[status(esa)],[f33_nnf]) ).
cnf(hi32,negated_conjecture,
product(a,c,u) = true,
inference(equality_encoding,[status(esa)],[c33]) ).
cnf(h541,plain,
product(c,a,u) = true,
inference(hyper_resolution,[status(thm)],[hi9,hi32]) ).
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(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(h45,plain,
product(multiplicative_identity,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi25]) ).
cnf(f16,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_multiplicative_identity) ).
fof(f16_nnf,plain,
defined(multiplicative_identity),
inference(nnf_transformation,[status(thm)],[f16]) ).
cnf(c16,plain,
defined(multiplicative_identity),
inference(cnf_transformation,[status(esa)],[f16_nnf]) ).
cnf(hi16,axiom,
defined(multiplicative_identity) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(h21,plain,
product(multiplicative_identity,multiplicative_identity,multiplicative_identity) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi16]) ).
cnf(f5,axiom,
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_multiplication_1) ).
fof(f5_nnf,plain,
! [X,V,W,Y,U,Z] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,V,W,Y,U,Z] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( ~ product(X4,X5,X2)
| ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X1,X3,X4),true,ifeq(product(X2,X3,X5),true,product(X0,X4,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(f31,negated_conjecture,
product(multiplicative_identity,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_6) ).
fof(f31_nnf,plain,
product(multiplicative_identity,a,b),
inference(nnf_transformation,[status(thm)],[f31]) ).
cnf(c31,plain,
product(multiplicative_identity,a,b),
inference(cnf_transformation,[status(esa)],[f31_nnf]) ).
cnf(hi30,negated_conjecture,
product(multiplicative_identity,a,b) = true,
inference(equality_encoding,[status(esa)],[c31]) ).
cnf(h1067,plain,
product(multiplicative_identity,b,a) = true,
inference(hyper_resolution,[status(thm)],[hi5,h21,hi30,h45]) ).
cnf(f32,negated_conjecture,
product(multiplicative_identity,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_7) ).
fof(f32_nnf,plain,
product(multiplicative_identity,c,d),
inference(nnf_transformation,[status(thm)],[f32]) ).
cnf(c32,plain,
product(multiplicative_identity,c,d),
inference(cnf_transformation,[status(esa)],[f32_nnf]) ).
cnf(hi31,negated_conjecture,
product(multiplicative_identity,c,d) = true,
inference(equality_encoding,[status(esa)],[c32]) ).
cnf(h540,plain,
product(c,multiplicative_identity,d) = true,
inference(hyper_resolution,[status(thm)],[hi9,hi31]) ).
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(t77,plain,
product(d,b,u) = true,
inference(hyper_resolution,[status(thm)],[hi6,h540,h1067,h541]) ).
cnf(t361,plain,
product(d,b,u) = true,
inference(orient,[status(thm)],[t77]) ).
cnf(t2411,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t232,t361]) ).
cnf(t111,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t111]) ).
cnf(t2412,plain,
false = true,
inference(step,[status(thm)],[t2411,t256]) ).
cnf(t2408,plain,
false = true,
inference(orient,[status(thm)],[t2412]) ).
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,c34]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2408]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD025-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n016.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 10:47:14 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 14.85/2.33 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.85/2.33 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------