%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COL074-3 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n007.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 01:01:59 PM UTC 2026
% Result : Unsatisfiable 42.79s 6.74s
% Output : Proof 42.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 32 unt; 0 def)
% Number of atoms : 46 ( 45 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 4 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 54 ( 6 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f12,axiom,
s = apply(eq,pair(apply(k,s),apply(k,projection2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',self_referential) ).
fof(f12_nnf,plain,
s = apply(eq,pair(apply(k,s),apply(k,projection2))),
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
s = apply(eq,pair(apply(k,s),apply(k,projection2))),
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(f7,axiom,
( apply(eq,pair(X,Y)) = projection2
| X = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality1) ).
fof(f7_nnf,plain,
! [X,Y] :
( apply(eq,pair(X,Y)) = projection2
| X = Y ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y] :
( apply(eq,pair(X,Y)) = projection2
| X = Y ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( apply(eq,pair(X0,X1)) = projection2
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(f4,axiom,
apply(pair(X,Y),Z) = pair(apply(X,Z),apply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pairwise_application) ).
fof(f4_nnf,plain,
! [X,Y,Z] : apply(pair(X,Y),Z) = pair(apply(X,Z),apply(Y,Z)),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y,Z] : apply(pair(X,Y),Z) = pair(apply(X,Z),apply(Y,Z)),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
apply(pair(X0,X1),X2) = pair(apply(X0,X2),apply(X1,X2)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(f0,negated_conjecture,
apply(apply(k,X),Y) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_definition) ).
fof(f0_nnf,plain,
! [X,Y] : apply(apply(k,X),Y) = X,
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] : apply(apply(k,X),Y) = X,
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
apply(apply(k,X0),X1) = X0,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p147,plain,
apply(pair(apply(k,X0),X1),X2) = pair(X0,apply(X1,X2)),
inference(superposition,[status(thm)],[c0,c4]) ).
cnf(p200,plain,
pair(apply(X0,X1),apply(X2,X1)) = apply(pair(X0,X2),X1),
inference(superposition,[status(thm)],[c4,p147]) ).
cnf(f3,axiom,
pair(apply(projection1,X),apply(projection2,X)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pairing) ).
fof(f3_nnf,plain,
! [X] : pair(apply(projection1,X),apply(projection2,X)) = X,
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X] : pair(apply(projection1,X),apply(projection2,X)) = X,
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
pair(apply(projection1,X0),apply(projection2,X0)) = X0,
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p180,plain,
apply(X0,X1) = pair(apply(apply(projection1,X0),X1),apply(apply(projection2,X0),X1)),
inference(superposition,[status(thm)],[c3,c4]) ).
cnf(p207,plain,
apply(X0,X1) = apply(pair(apply(projection1,X0),apply(projection2,X0)),X1),
inference(demodulation,[status(thm)],[p200,p180]) ).
cnf(p325,plain,
( projection2 = apply(eq,pair(X0,X1))
| X0 = X1 ),
inference(superposition,[status(thm)],[c7,p207]) ).
cnf(p540,plain,
( projection2 = s
| apply(k,s) = k_projection2 ),
inference(superposition,[status(thm)],[c12,p325]) ).
cnf(p692,plain,
( projection2 = s
| projection2 = s ),
inference(superposition,[status(thm)],[p540,c0]) ).
cnf(p713,plain,
projection2 = s,
inference(factoring,[status(thm)],[p692]) ).
cnf(p855,plain,
s = projection1,
inference(superposition,[status(thm)],[p713,c12]) ).
cnf(p866,plain,
projection2 = projection1,
inference(demodulation,[status(thm)],[p855,p713]) ).
cnf(f2,axiom,
apply(projection2,pair(X,Y)) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',projection2) ).
fof(f2_nnf,plain,
! [X,Y] : apply(projection2,pair(X,Y)) = Y,
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y] : apply(projection2,pair(X,Y)) = Y,
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
apply(projection2,pair(X0,X1)) = X1,
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p868,plain,
X0 = X1,
inference(superposition,[status(thm)],[p866,c2]) ).
cnf(f9,axiom,
projection1 != projection2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',different_projections) ).
fof(f9_nnf,plain,
projection1 != projection2,
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
projection1 != projection2,
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
projection1 != projection2,
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p869,plain,
$false,
inference(resolution,[status(thm)],[p868,c9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL074-3 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.13/0.38 % Computer : n007.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Fri Sep 25 07:27:23 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 42.79/6.74 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 42.79/6.74 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------