%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : FLD071-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.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 01:15:09 PM UTC 2026
% Result : Unsatisfiable 6.87s 1.46s
% Output : Proof 6.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 53 ( 45 unt; 0 def)
% Number of atoms : 69 ( 27 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 42 ( 26 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-4 aty)
% Number of variables : 42 ( 2 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f24,axiom,
( ~ product(X,Y,Z)
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatibility_of_order_relation_and_multiplication) ).
fof(f24_nnf,plain,
! [Z,X,Y] :
( ~ product(X,Y,Z)
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [Z,X,Y] :
( ~ product(X,Y,Z)
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
( ~ product(X1,X2,X0)
| ~ less_or_equal(additive_identity,X2)
| ~ less_or_equal(additive_identity,X1)
| less_or_equal(additive_identity,X0) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(t32,plain,
ifeq(less_or_equal(additive_identity,X1),true,ifeq(less_or_equal(additive_identity,X2),true,ifeq(product(X1,X2,X3),true,less_or_equal(additive_identity,X3),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(t70,plain,
ifeq(less_or_equal(additive_identity,X1),true,ifeq(less_or_equal(additive_identity,X2),true,ifeq(product(X1,X2,X3),true,less_or_equal(additive_identity,X3),true),true),true) = true,
inference(orient,[status(thm)],[t32]) ).
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(t21,plain,
ifeq(product(X1,X2,X3),true,product(X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t64,plain,
ifeq(product(X1,X2,X3),true,product(X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t21]) ).
cnf(f31,negated_conjecture,
product(a,b,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_6) ).
fof(f31_nnf,plain,
product(a,b,u),
inference(nnf_transformation,[status(thm)],[f31]) ).
cnf(c31,plain,
product(a,b,u),
inference(cnf_transformation,[status(esa)],[f31_nnf]) ).
cnf(t12,plain,
product(a,b,u) = true,
inference(equality_encoding,[status(esa)],[c31]) ).
cnf(t157,plain,
product(a,b,u) = true,
inference(orient,[status(thm)],[t12]) ).
cnf(t158,plain,
true = ifeq(true,true,product(b,a,u),true),
inference(cp,[status(thm)],[t64,t157]) ).
cnf(t14,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t40,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t14]) ).
cnf(t561,plain,
true = product(b,a,u),
inference(step,[status(thm)],[t158,t40]) ).
cnf(t516,plain,
product(b,a,u) = true,
inference(orient,[status(thm)],[t561]) ).
cnf(t517,plain,
true = ifeq(less_or_equal(additive_identity,b),true,ifeq(less_or_equal(additive_identity,a),true,ifeq(true,true,less_or_equal(additive_identity,u),true),true),true),
inference(cp,[status(thm)],[t70,t516]) ).
cnf(f30,negated_conjecture,
less_or_equal(additive_identity,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_5) ).
fof(f30_nnf,plain,
less_or_equal(additive_identity,b),
inference(nnf_transformation,[status(thm)],[f30]) ).
cnf(c30,plain,
less_or_equal(additive_identity,b),
inference(cnf_transformation,[status(esa)],[f30_nnf]) ).
cnf(t6,plain,
less_or_equal(additive_identity,b) = true,
inference(equality_encoding,[status(esa)],[c30]) ).
cnf(t188,plain,
less_or_equal(additive_identity,b) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t562,plain,
true = ifeq(true,true,ifeq(less_or_equal(additive_identity,a),true,ifeq(true,true,less_or_equal(additive_identity,u),true),true),true),
inference(step,[status(thm)],[t517,t188]) ).
cnf(t563,plain,
true = ifeq(less_or_equal(additive_identity,a),true,ifeq(true,true,less_or_equal(additive_identity,u),true),true),
inference(step,[status(thm)],[t562,t40]) ).
cnf(f29,negated_conjecture,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_4) ).
fof(f29_nnf,plain,
less_or_equal(additive_identity,a),
inference(nnf_transformation,[status(thm)],[f29]) ).
cnf(c29,plain,
less_or_equal(additive_identity,a),
inference(cnf_transformation,[status(esa)],[f29_nnf]) ).
cnf(t5,plain,
less_or_equal(additive_identity,a) = true,
inference(equality_encoding,[status(esa)],[c29]) ).
cnf(t175,plain,
less_or_equal(additive_identity,a) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t564,plain,
true = ifeq(true,true,ifeq(true,true,less_or_equal(additive_identity,u),true),true),
inference(step,[status(thm)],[t563,t175]) ).
cnf(t565,plain,
true = ifeq(true,true,less_or_equal(additive_identity,u),true),
inference(step,[status(thm)],[t564,t40]) ).
cnf(t566,plain,
true = less_or_equal(additive_identity,u),
inference(step,[status(thm)],[t565,t40]) ).
cnf(f32,negated_conjecture,
~ less_or_equal(additive_identity,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_7) ).
fof(f32_nnf,plain,
~ less_or_equal(additive_identity,u),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
~ less_or_equal(additive_identity,u),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c32,plain,
~ less_or_equal(additive_identity,u),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(t7,plain,
less_or_equal(additive_identity,u) = false,
inference(equality_encoding,[status(esa)],[c32]) ).
cnf(t222,plain,
less_or_equal(additive_identity,u) = false,
inference(orient,[status(thm)],[t7]) ).
cnf(t567,plain,
true = false,
inference(step,[status(thm)],[t566,t222]) ).
cnf(t532,plain,
false = true,
inference(orient,[status(thm)],[t567]) ).
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,t532]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD071-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 11:05:02 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.87/1.46 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.87/1.46 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------