%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COL077-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.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 49.16s 6.56s
% Output : Proof 49.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 10
% Syntax : Number of formulae : 75 ( 67 unt; 0 def)
% Number of atoms : 83 ( 82 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 22 ( 14 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-4 aty)
% Number of variables : 106 ( 14 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t15,plain,
or(eqq(X1,X2),eqq(apply(eq,pair(X1,X2)),projection2)) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t65,plain,
or(eqq(X1,X2),eqq(apply(eq,pair(X1,X2)),projection2)) = true,
inference(orient,[status(thm)],[t15]) ).
cnf(f11,negated_conjecture,
apply(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),abstraction),abstraction) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_TRC1a) ).
fof(f11_nnf,plain,
apply(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),abstraction),abstraction) != identity,
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
apply(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),abstraction),abstraction) != identity,
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
apply(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),abstraction),abstraction) != identity,
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t17,plain,
eqq(apply(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),abstraction),abstraction),identity) = false,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t69,plain,
eqq(apply(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),abstraction),abstraction),identity) = false,
inference(orient,[status(thm)],[t17]) ).
cnf(t71,plain,
true = or(false,eqq(apply(eq,pair(apply(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),abstraction),abstraction),identity)),projection2)),
inference(cp,[status(thm)],[t65,t69]) ).
cnf(t5,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t27,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t33645,plain,
true = eqq(apply(eq,pair(apply(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),abstraction),abstraction),identity)),projection2),
inference(step,[status(thm)],[t71,t27]) ).
cnf(f5,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(f5_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)],[f5]) ).
fof(f5_sk,plain,
! [X,Y,Z] : apply(apply(apply(abstraction,X),Y),Z) = apply(apply(X,k(Z)),apply(Y,Z)),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
apply(apply(apply(abstraction,X0),X1),X2) = apply(apply(X0,k(X2)),apply(X1,X2)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t19,plain,
apply(apply(X1,k(X2)),apply(X3,X2)) = apply(apply(apply(abstraction,X1),X3),X2),
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t35,plain,
apply(apply(X1,k(X2)),apply(X3,X2)) = apply(apply(apply(abstraction,X1),X3),X2),
inference(orient,[status(thm)],[t19]) ).
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(t7,plain,
apply(k(X1),X2) = X1,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t24,plain,
apply(k(X1),X2) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t36,plain,
apply(apply(apply(abstraction,k(X1)),X2),X3) = apply(X1,apply(X2,X3)),
inference(cp,[status(thm)],[t35,t24]) ).
cnf(t311,plain,
apply(apply(apply(abstraction,k(X1)),X2),X3) = apply(X1,apply(X2,X3)),
inference(orient,[status(thm)],[t36]) ).
cnf(t313,plain,
apply(X1,apply(apply(X2,X1),X3)) = apply(apply(apply(apply(abstraction,abstraction),X2),X1),X3),
inference(cp,[status(thm)],[t311,t35]) ).
cnf(t2962,plain,
apply(X1,apply(apply(X2,X1),X3)) = apply(apply(apply(apply(abstraction,abstraction),X2),X1),X3),
inference(orient,[status(thm)],[t313]) ).
cnf(t33646,plain,
true = eqq(apply(eq,pair(apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction),identity)),projection2),
inference(step,[status(thm)],[t33645,t2962]) ).
cnf(f8,axiom,
( apply(X,n(X,Y)) != apply(Y,n(X,Y))
| X = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality2) ).
fof(f8_nnf,plain,
! [X,Y] :
( apply(X,n(X,Y)) != apply(Y,n(X,Y))
| X = Y ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y] :
( apply(X,n(X,Y)) != apply(Y,n(X,Y))
| X = Y ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( apply(X0,n(X0,X1)) != apply(X1,n(X0,X1))
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t18,plain,
ifeq(apply(X1,n(X1,X2)),apply(X2,n(X1,X2)),X1,X2) = X2,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t29,plain,
ifeq(apply(X1,n(X1,X2)),apply(X2,n(X1,X2)),X1,X2) = X2,
inference(orient,[status(thm)],[t18]) ).
cnf(f10,axiom,
apply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_definition) ).
fof(f10_nnf,plain,
! [X] : apply(identity,X) = X,
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X] : apply(identity,X) = X,
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
apply(identity,X0) = X0,
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t0,plain,
apply(identity,X1) = X1,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t23,plain,
apply(identity,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t31,plain,
X1 = ifeq(n(identity,X1),apply(X1,n(identity,X1)),identity,X1),
inference(cp,[status(thm)],[t29,t23]) ).
cnf(t1394,plain,
ifeq(n(identity,X1),apply(X1,n(identity,X1)),identity,X1) = X1,
inference(orient,[status(thm)],[t31]) ).
cnf(t2972,plain,
apply(apply(apply(apply(abstraction,abstraction),X1),k(X2)),apply(X3,X2)) = apply(k(X2),apply(apply(apply(abstraction,X1),X3),X2)),
inference(cp,[status(thm)],[t2962,t35]) ).
cnf(t33521,plain,
apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),X1)),X3),X2) = apply(k(X2),apply(apply(apply(abstraction,X1),X3),X2)),
inference(step,[status(thm)],[t2972,t35]) ).
cnf(t33522,plain,
apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),X1)),X3),X2) = X2,
inference(step,[status(thm)],[t33521,t24]) ).
cnf(t9308,plain,
apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),X1)),X2),X3) = X3,
inference(orient,[status(thm)],[t33522]) ).
cnf(t9355,plain,
apply(apply(abstraction,apply(apply(abstraction,abstraction),X1)),X2) = ifeq(n(identity,apply(apply(abstraction,apply(apply(abstraction,abstraction),X1)),X2)),n(identity,apply(apply(abstraction,apply(apply(abstraction,abstraction),X1)),X2)),identity,apply(apply(abstraction,apply(apply(abstraction,abstraction),X1)),X2)),
inference(cp,[status(thm)],[t1394,t9308]) ).
cnf(t11,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t28,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(t33523,plain,
apply(apply(abstraction,apply(apply(abstraction,abstraction),X1)),X2) = identity,
inference(step,[status(thm)],[t9355,t28]) ).
cnf(t9370,plain,
apply(apply(abstraction,apply(apply(abstraction,abstraction),X1)),X2) = identity,
inference(orient,[status(thm)],[t33523]) ).
cnf(t33647,plain,
true = eqq(apply(eq,pair(identity,identity)),projection2),
inference(step,[status(thm)],[t33646,t9370]) ).
cnf(f6,axiom,
apply(eq,pair(X,X)) = projection1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equality) ).
fof(f6_nnf,plain,
! [X] : apply(eq,pair(X,X)) = projection1,
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X] : apply(eq,pair(X,X)) = projection1,
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
apply(eq,pair(X0,X0)) = projection1,
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t8,plain,
apply(eq,pair(X1,X1)) = projection1,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t57,plain,
apply(eq,pair(X1,X1)) = projection1,
inference(orient,[status(thm)],[t8]) ).
cnf(t33648,plain,
true = eqq(projection1,projection2),
inference(step,[status(thm)],[t33647,t57]) ).
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(t2,plain,
eqq(projection1,projection2) = false,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t72,plain,
eqq(projection1,projection2) = false,
inference(orient,[status(thm)],[t2]) ).
cnf(t33649,plain,
true = false,
inference(step,[status(thm)],[t33648,t72]) ).
cnf(t33420,plain,
false = true,
inference(orient,[status(thm)],[t33649]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c9,c11]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t33420]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : COL077-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Fri Sep 25 07:29:20 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.29 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 49.16/6.56 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 49.16/6.56 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------