%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COL081-2 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.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 01:02:00 PM UTC 2026
% Result : Unsatisfiable 5.45s 1.22s
% Output : Proof 5.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 47 ( 43 unt; 0 def)
% Number of atoms : 51 ( 50 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 10 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-4 aty)
% Number of variables : 96 ( 16 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f2,axiom,
( apply(X,n(X,Y)) != apply(Y,n(X,Y))
| X = Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality2) ).
fof(f2_nnf,plain,
! [X,Y] :
( apply(X,n(X,Y)) != apply(Y,n(X,Y))
| X = Y ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y] :
( apply(X,n(X,Y)) != apply(Y,n(X,Y))
| X = Y ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( apply(X0,n(X0,X1)) != apply(X1,n(X0,X1))
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t3,plain,
ifeq(apply(X1,n(X1,X2)),apply(X2,n(X1,X2)),X1,X2) = X2,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t8,plain,
ifeq(apply(X1,n(X1,X2)),apply(X2,n(X1,X2)),X1,X2) = X2,
inference(orient,[status(thm)],[t3]) ).
cnf(f0,axiom,
apply(k(X),Y) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).
fof(f0_nnf,plain,
! [X,Y] : apply(k(X),Y) = X,
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] : apply(k(X),Y) = X,
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
apply(k(X0),X1) = X0,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t1,plain,
apply(k(X1),X2) = X1,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t5,plain,
apply(k(X1),X2) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t11,plain,
k(X1) = ifeq(apply(X2,n(X2,k(X1))),X1,X2,k(X1)),
inference(cp,[status(thm)],[t8,t5]) ).
cnf(t84,plain,
ifeq(apply(X1,n(X1,k(X2))),X2,X1,k(X2)) = k(X2),
inference(orient,[status(thm)],[t11]) ).
cnf(f1,axiom,
apply(apply(apply(abstraction,X),Y),Z) = apply(apply(X,k(Z)),apply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstraction) ).
fof(f1_nnf,plain,
! [X,Y,Z] : apply(apply(apply(abstraction,X),Y),Z) = apply(apply(X,k(Z)),apply(Y,Z)),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y,Z] : apply(apply(apply(abstraction,X),Y),Z) = apply(apply(X,k(Z)),apply(Y,Z)),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
apply(apply(apply(abstraction,X0),X1),X2) = apply(apply(X0,k(X2)),apply(X1,X2)),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t4,plain,
apply(apply(X1,k(X2)),apply(X3,X2)) = apply(apply(apply(abstraction,X1),X3),X2),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t13,plain,
apply(apply(X1,k(X2)),apply(X3,X2)) = apply(apply(apply(abstraction,X1),X3),X2),
inference(orient,[status(thm)],[t4]) ).
cnf(t14,plain,
apply(apply(apply(abstraction,k(X1)),X2),X3) = apply(X1,apply(X2,X3)),
inference(cp,[status(thm)],[t13,t5]) ).
cnf(t25,plain,
apply(apply(apply(abstraction,k(X1)),X2),X3) = apply(X1,apply(X2,X3)),
inference(orient,[status(thm)],[t14]) ).
cnf(t27,plain,
apply(X1,apply(apply(X2,X1),X3)) = apply(apply(apply(apply(abstraction,abstraction),X2),X1),X3),
inference(cp,[status(thm)],[t25,t13]) ).
cnf(t410,plain,
apply(X1,apply(apply(X2,X1),X3)) = apply(apply(apply(apply(abstraction,abstraction),X2),X1),X3),
inference(orient,[status(thm)],[t27]) ).
cnf(t419,plain,
apply(apply(apply(apply(abstraction,abstraction),X1),k(X2)),X3) = X2,
inference(cp,[status(thm)],[t410,t5]) ).
cnf(t496,plain,
apply(apply(apply(apply(abstraction,abstraction),X1),k(X2)),X3) = X2,
inference(orient,[status(thm)],[t419]) ).
cnf(t510,plain,
k(X1) = ifeq(X2,X1,apply(apply(apply(abstraction,abstraction),X3),k(X2)),k(X1)),
inference(cp,[status(thm)],[t84,t496]) ).
cnf(t643,plain,
ifeq(X1,X2,apply(apply(apply(abstraction,abstraction),X3),k(X1)),k(X2)) = k(X2),
inference(orient,[status(thm)],[t510]) ).
cnf(t2,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t7,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t2]) ).
cnf(t644,plain,
k(X1) = apply(apply(apply(abstraction,abstraction),X2),k(X1)),
inference(cp,[status(thm)],[t643,t7]) ).
cnf(t647,plain,
apply(apply(apply(abstraction,abstraction),X1),k(X2)) = k(X2),
inference(orient,[status(thm)],[t644]) ).
cnf(t16,plain,
apply(apply(apply(abstraction,X1),k(X2)),X3) = apply(apply(X1,k(X3)),X2),
inference(cp,[status(thm)],[t13,t5]) ).
cnf(t38,plain,
apply(apply(apply(abstraction,X1),k(X2)),X3) = apply(apply(X1,k(X3)),X2),
inference(orient,[status(thm)],[t16]) ).
cnf(t648,plain,
k(X1) = apply(apply(abstraction,k(k(X1))),X2),
inference(cp,[status(thm)],[t647,t38]) ).
cnf(t656,plain,
apply(apply(abstraction,k(k(X1))),X2) = k(X1),
inference(orient,[status(thm)],[t648]) ).
cnf(t665,plain,
k(X1) = ifeq(k(X2),X1,apply(abstraction,k(k(X2))),k(X1)),
inference(cp,[status(thm)],[t84,t656]) ).
cnf(t669,plain,
ifeq(k(X1),X2,apply(abstraction,k(k(X1))),k(X2)) = k(X2),
inference(orient,[status(thm)],[t665]) ).
cnf(t670,plain,
k(k(X1)) = apply(abstraction,k(k(X1))),
inference(cp,[status(thm)],[t669,t7]) ).
cnf(t671,plain,
apply(abstraction,k(k(X1))) = k(k(X1)),
inference(orient,[status(thm)],[t670]) ).
cnf(f4,negated_conjecture,
k(k(b)) != apply(abstraction,k(k(b))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_TRC2c) ).
fof(f4_nnf,plain,
k(k(b)) != apply(abstraction,k(k(b))),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
k(k(b)) != apply(abstraction,k(k(b))),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
k(k(b)) != apply(abstraction,k(k(b))),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(goal_0,negated_conjecture,
apply(abstraction,k(k(b))) != k(k(b)),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(g0_0,plain,
k(k(b)) != k(k(b)),
inference(rw,[status(thm)],[goal_0,t671]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL081-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.35 % Computer : n017.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Fri Sep 25 07:26:17 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.45/1.22 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.45/1.22 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------