%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COL079-2 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n002.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 45.43s 6.50s
% Output : Proof 45.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 8
% Syntax : Number of formulae : 65 ( 61 unt; 0 def)
% Number of atoms : 69 ( 68 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 13 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 84 ( 6 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t4,axiom,
sFlat0 = apply(abstraction,b),
introduced(definition) ).
cnf(t21,plain,
apply(abstraction,b) = sFlat0,
inference(orient,[status(thm)],[t4]) ).
cnf(t5,axiom,
sFlat1 = apply(abstraction,apply(abstraction,b)),
introduced(definition) ).
cnf(t18,plain,
apply(abstraction,apply(abstraction,b)) = sFlat1,
inference(orient,[status(thm)],[t5]) ).
cnf(t79202,plain,
apply(abstraction,sFlat0) = sFlat1,
inference(step,[status(thm)],[t18,t21]) ).
cnf(t23,plain,
apply(abstraction,sFlat0) = sFlat1,
inference(rw,[status(thm)],[t79202]) ).
cnf(t26,plain,
apply(abstraction,sFlat0) = sFlat1,
inference(orient,[status(thm)],[t23]) ).
cnf(t6,axiom,
sFlat2 = apply(abstraction,apply(abstraction,apply(abstraction,b))),
introduced(definition) ).
cnf(t16,plain,
apply(abstraction,apply(abstraction,apply(abstraction,b))) = sFlat2,
inference(orient,[status(thm)],[t6]) ).
cnf(t79201,plain,
apply(abstraction,sFlat1) = sFlat2,
inference(step,[status(thm)],[t16,t18]) ).
cnf(t20,plain,
apply(abstraction,sFlat1) = sFlat2,
inference(rw,[status(thm)],[t79201]) ).
cnf(t24,plain,
apply(abstraction,sFlat1) = sFlat2,
inference(orient,[status(thm)],[t20]) ).
cnf(f2,axiom,
( apply(X,n(X,Y)) != apply(Y,n(X,Y))
| X = Y ),
file('/export/starexec/sandbox2/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(t2,plain,
ifeq(apply(X1,n(X1,X2)),apply(X2,n(X1,X2)),X1,X2) = X2,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t9,plain,
ifeq(apply(X1,n(X1,X2)),apply(X2,n(X1,X2)),X1,X2) = X2,
inference(orient,[status(thm)],[t2]) ).
cnf(f1,axiom,
apply(apply(apply(abstraction,X),Y),Z) = apply(apply(X,k(Z)),apply(Y,Z)),
file('/export/starexec/sandbox2/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(t3,plain,
apply(apply(X1,k(X2)),apply(X3,X2)) = apply(apply(apply(abstraction,X1),X3),X2),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t12,plain,
apply(apply(X1,k(X2)),apply(X3,X2)) = apply(apply(apply(abstraction,X1),X3),X2),
inference(orient,[status(thm)],[t3]) ).
cnf(f0,axiom,
apply(k(X),Y) = X,
file('/export/starexec/sandbox2/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(t0,plain,
apply(k(X1),X2) = X1,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t7,plain,
apply(k(X1),X2) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t14,plain,
apply(apply(apply(abstraction,X1),k(X2)),X3) = apply(apply(X1,k(X3)),X2),
inference(cp,[status(thm)],[t12,t7]) ).
cnf(t68,plain,
apply(apply(apply(abstraction,X1),k(X2)),X3) = apply(apply(X1,k(X3)),X2),
inference(orient,[status(thm)],[t14]) ).
cnf(t71,plain,
apply(apply(b,k(X1)),X2) = apply(apply(sFlat0,k(X2)),X1),
inference(cp,[status(thm)],[t68,t21]) ).
cnf(t107,plain,
apply(apply(b,k(X1)),X2) = apply(apply(sFlat0,k(X2)),X1),
inference(orient,[status(thm)],[t71]) ).
cnf(t70,plain,
apply(apply(sFlat0,k(X1)),X2) = apply(apply(sFlat1,k(X2)),X1),
inference(cp,[status(thm)],[t68,t26]) ).
cnf(t93,plain,
apply(apply(sFlat0,k(X1)),X2) = apply(apply(sFlat1,k(X2)),X1),
inference(orient,[status(thm)],[t70]) ).
cnf(t110,plain,
apply(apply(b,k(X1)),X2) = apply(apply(sFlat1,k(X1)),X2),
inference(cp,[status(thm)],[t107,t93]) ).
cnf(t128,plain,
apply(apply(b,k(X1)),X2) = apply(apply(sFlat1,k(X1)),X2),
inference(orient,[status(thm)],[t110]) ).
cnf(t129,plain,
apply(apply(sFlat1,k(X1)),apply(X2,X1)) = apply(apply(apply(abstraction,b),X2),X1),
inference(cp,[status(thm)],[t128,t12]) ).
cnf(t79220,plain,
apply(apply(apply(abstraction,sFlat1),X2),X1) = apply(apply(apply(abstraction,b),X2),X1),
inference(step,[status(thm)],[t129,t12]) ).
cnf(t79221,plain,
apply(apply(sFlat2,X2),X1) = apply(apply(apply(abstraction,b),X2),X1),
inference(step,[status(thm)],[t79220,t24]) ).
cnf(t79222,plain,
apply(apply(sFlat2,X2),X1) = apply(apply(sFlat0,X2),X1),
inference(step,[status(thm)],[t79221,t21]) ).
cnf(t137,plain,
apply(apply(sFlat2,X1),X2) = apply(apply(sFlat0,X1),X2),
inference(orient,[status(thm)],[t79222]) ).
cnf(t139,plain,
X1 = ifeq(apply(apply(sFlat0,X2),n(apply(sFlat2,X2),X1)),apply(X1,n(apply(sFlat2,X2),X1)),apply(sFlat2,X2),X1),
inference(cp,[status(thm)],[t9,t137]) ).
cnf(t76286,plain,
ifeq(apply(apply(sFlat0,X1),n(apply(sFlat2,X1),X2)),apply(X2,n(apply(sFlat2,X1),X2)),apply(sFlat2,X1),X2) = X2,
inference(orient,[status(thm)],[t139]) ).
cnf(t1,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t8,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t1]) ).
cnf(t76287,plain,
apply(sFlat0,X1) = apply(sFlat2,X1),
inference(cp,[status(thm)],[t76286,t8]) ).
cnf(t76536,plain,
apply(sFlat2,X1) = apply(sFlat0,X1),
inference(orient,[status(thm)],[t76287]) ).
cnf(t76538,plain,
X1 = ifeq(apply(sFlat0,n(sFlat2,X1)),apply(X1,n(sFlat2,X1)),sFlat2,X1),
inference(cp,[status(thm)],[t9,t76536]) ).
cnf(t78951,plain,
ifeq(apply(sFlat0,n(sFlat2,X1)),apply(X1,n(sFlat2,X1)),sFlat2,X1) = X1,
inference(orient,[status(thm)],[t76538]) ).
cnf(t78952,plain,
sFlat0 = sFlat2,
inference(cp,[status(thm)],[t78951,t8]) ).
cnf(t79087,plain,
sFlat2 = sFlat0,
inference(orient,[status(thm)],[t78952]) ).
cnf(t80111,plain,
apply(abstraction,sFlat1) = sFlat0,
inference(step,[status(thm)],[t24,t79087]) ).
cnf(t79088,plain,
apply(abstraction,sFlat1) = sFlat0,
inference(orient,[status(thm)],[t80111]) ).
cnf(f3,negated_conjecture,
apply(abstraction,apply(abstraction,apply(abstraction,b))) != apply(abstraction,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_TRC2a) ).
fof(f3_nnf,plain,
apply(abstraction,apply(abstraction,apply(abstraction,b))) != apply(abstraction,b),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
apply(abstraction,apply(abstraction,apply(abstraction,b))) != apply(abstraction,b),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
apply(abstraction,apply(abstraction,apply(abstraction,b))) != apply(abstraction,b),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(goal_0,negated_conjecture,
apply(abstraction,apply(abstraction,apply(abstraction,b))) != apply(abstraction,b),
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(g0_0,plain,
apply(abstraction,apply(abstraction,sFlat0)) != apply(abstraction,b),
inference(rw,[status(thm)],[goal_0,t21]) ).
cnf(g0_1,plain,
apply(abstraction,sFlat1) != apply(abstraction,b),
inference(rw,[status(thm)],[g0_0,t26]) ).
cnf(g0_2,plain,
sFlat0 != apply(abstraction,b),
inference(rw,[status(thm)],[g0_1,t79088]) ).
cnf(g0_3,plain,
sFlat0 != sFlat0,
inference(rw,[status(thm)],[g0_2,t21]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL079-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.35 % Computer : n002.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 07:33:05 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 45.43/6.50 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 45.43/6.50 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------