%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : FLD068-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/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 01:15:08 PM UTC 2026
% Result : Unsatisfiable 109.86s 14.49s
% Output : Proof 109.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of formulae : 82 ( 54 unt; 0 def)
% Number of atoms : 130 ( 36 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 106 ( 58 ~; 48 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 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 : 112 ( 2 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f23,axiom,
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatibility_of_order_relation_and_addition) ).
fof(f23_nnf,plain,
! [U,V,X,Y,Z] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [U,V,X,Y,Z] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( ~ sum(X3,X4,X1)
| ~ sum(X2,X4,X0)
| ~ less_or_equal(X2,X3)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(t249,plain,
ifeq(less_or_equal(X1,X2),true,ifeq(sum(X1,X3,X4),true,ifeq(sum(X2,X3,X5),true,less_or_equal(X4,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t498,plain,
ifeq(less_or_equal(X1,X2),true,ifeq(sum(X1,X3,X4),true,ifeq(sum(X2,X3,X5),true,less_or_equal(X4,X5),true),true),true) = true,
inference(orient,[status(thm)],[t249]) ).
cnf(f2,axiom,
( ~ defined(X)
| sum(additive_identity,X,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_addition) ).
fof(f2_nnf,plain,
! [X] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(defined(X0),true,sum(additive_identity,X0,X0),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(f26,hypothesis,
defined(a),
file('/export/starexec/sandbox2/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(t24,plain,
sum(additive_identity,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi25]) ).
cnf(t364,plain,
sum(additive_identity,a,a) = true,
inference(orient,[status(thm)],[t24]) ).
cnf(t508,plain,
true = ifeq(less_or_equal(additive_identity,X1),true,ifeq(true,true,ifeq(sum(X1,a,X2),true,less_or_equal(a,X2),true),true),true),
inference(cp,[status(thm)],[t498,t364]) ).
cnf(t28,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t258,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t28]) ).
cnf(t24948,plain,
true = ifeq(less_or_equal(additive_identity,X1),true,ifeq(sum(X1,a,X2),true,less_or_equal(a,X2),true),true),
inference(step,[status(thm)],[t508,t258]) ).
cnf(t23847,plain,
ifeq(less_or_equal(additive_identity,X1),true,ifeq(sum(X1,a,X2),true,less_or_equal(a,X2),true),true) = true,
inference(orient,[status(thm)],[t24948]) ).
cnf(f27,hypothesis,
defined(b),
file('/export/starexec/sandbox2/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(h103,plain,
sum(additive_identity,b,b) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi26]) ).
cnf(f4,axiom,
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_addition) ).
fof(f4_nnf,plain,
! [Y,X,Z] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [Y,X,Z] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,axiom,
ifeq(sum(X0,X1,X2),true,sum(X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h8381,plain,
sum(b,additive_identity,b) = true,
inference(hyper_resolution,[status(thm)],[hi4,h103]) ).
cnf(f3,axiom,
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_addition) ).
fof(f3_nnf,plain,
! [X] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( ~ defined(X0)
| sum(additive_inverse(X0),X0,additive_identity) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
ifeq(defined(X0),true,sum(additive_inverse(X0),X0,additive_identity),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h61,plain,
sum(additive_inverse(a),a,additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi25]) ).
cnf(f14,axiom,
( ~ defined(X)
| defined(additive_inverse(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
fof(f14_nnf,plain,
! [X] :
( ~ defined(X)
| defined(additive_inverse(X)) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X] :
( ~ defined(X)
| defined(additive_inverse(X)) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( ~ defined(X0)
| defined(additive_inverse(X0)) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi14,axiom,
ifeq(defined(X0),true,defined(additive_inverse(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(h53,plain,
defined(additive_inverse(a)) = true,
inference(hyper_resolution,[status(thm)],[hi14,hi25]) ).
cnf(f18,axiom,
( ~ defined(Y)
| ~ defined(X)
| sum(X,Y,add(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality_of_addition) ).
fof(f18_nnf,plain,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| sum(X,Y,add(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| sum(X,Y,add(X,Y)) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( ~ defined(X1)
| ~ defined(X0)
| sum(X0,X1,add(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi18,axiom,
ifeq(defined(X0),true,ifeq(defined(X1),true,sum(X0,X1,add(X0,X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(h407,plain,
sum(b,additive_inverse(a),add(b,additive_inverse(a))) = true,
inference(hyper_resolution,[status(thm)],[hi18,hi26,h53]) ).
cnf(f1,axiom,
( ~ sum(X,V,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(U,Z,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_addition_2) ).
fof(f1_nnf,plain,
! [U,Z,W,X,Y,V] :
( ~ sum(X,V,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(U,Z,W) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [U,Z,W,X,Y,V] :
( ~ sum(X,V,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(U,Z,W) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( ~ sum(X3,X5,X2)
| ~ sum(X4,X1,X5)
| ~ sum(X3,X4,X0)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,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)],[c1]) ).
cnf(t101,plain,
sum(add(b,additive_inverse(a)),a,b) = true,
inference(hyper_resolution,[status(thm)],[hi1,h407,h61,h8381]) ).
cnf(t361,plain,
sum(add(b,additive_inverse(a)),a,b) = true,
inference(orient,[status(thm)],[t101]) ).
cnf(t23854,plain,
true = ifeq(less_or_equal(additive_identity,add(b,additive_inverse(a))),true,ifeq(true,true,less_or_equal(a,b),true),true),
inference(cp,[status(thm)],[t23847,t361]) ).
cnf(f28,negated_conjecture,
less_or_equal(additive_identity,add(b,additive_inverse(a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_3) ).
fof(f28_nnf,plain,
less_or_equal(additive_identity,add(b,additive_inverse(a))),
inference(nnf_transformation,[status(thm)],[f28]) ).
cnf(c28,plain,
less_or_equal(additive_identity,add(b,additive_inverse(a))),
inference(cnf_transformation,[status(esa)],[f28_nnf]) ).
cnf(t74,plain,
less_or_equal(additive_identity,add(b,additive_inverse(a))) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(t259,plain,
less_or_equal(additive_identity,add(b,additive_inverse(a))) = true,
inference(orient,[status(thm)],[t74]) ).
cnf(t24949,plain,
true = ifeq(true,true,ifeq(true,true,less_or_equal(a,b),true),true),
inference(step,[status(thm)],[t23854,t259]) ).
cnf(t24950,plain,
true = ifeq(true,true,less_or_equal(a,b),true),
inference(step,[status(thm)],[t24949,t258]) ).
cnf(t24951,plain,
true = less_or_equal(a,b),
inference(step,[status(thm)],[t24950,t258]) ).
cnf(f29,negated_conjecture,
~ less_or_equal(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_less_or_equal_4) ).
fof(f29_nnf,plain,
~ less_or_equal(a,b),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
~ less_or_equal(a,b),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c29,plain,
~ less_or_equal(a,b),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(t6,plain,
less_or_equal(a,b) = false,
inference(equality_encoding,[status(esa)],[c29]) ).
cnf(t3187,plain,
less_or_equal(a,b) = false,
inference(orient,[status(thm)],[t6]) ).
cnf(t24952,plain,
true = false,
inference(step,[status(thm)],[t24951,t3187]) ).
cnf(t23866,plain,
false = true,
inference(orient,[status(thm)],[t24952]) ).
cnf(f25,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
file('/export/starexec/sandbox2/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,c29]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t23866]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD068-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 11:04:26 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 109.86/14.49 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 109.86/14.49 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------