%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COL075-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 8.83s 6.89s
% Output : Proof 8.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 35 unt; 0 def)
% Number of atoms : 35 ( 34 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 10 ( 10 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 50 ( 6 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f10,negated_conjecture,
apply(apply(Y,b(Y)),c(Y)) != apply(b(Y),b(Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_diagonal_combinator) ).
fof(f10_nnf,plain,
! [Y] : apply(apply(Y,b(Y)),c(Y)) != apply(b(Y),b(Y)),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [Y] : apply(apply(Y,b(Y)),c(Y)) != apply(b(Y),b(Y)),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
apply(apply(X0,b(X0)),c(X0)) != apply(b(X0),b(X0)),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t16,plain,
eqq(apply(apply(X1,b(X1)),c(X1)),apply(b(X1),b(X1))) = false,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t65,plain,
eqq(apply(apply(X1,b(X1)),c(X1)),apply(b(X1),b(X1))) = false,
inference(orient,[status(thm)],[t16]) ).
cnf(f5,axiom,
apply(apply(apply(abstraction,X),Y),Z) = apply(apply(X,apply(k,Z)),apply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstraction) ).
fof(f5_nnf,plain,
! [X,Y,Z] : apply(apply(apply(abstraction,X),Y),Z) = apply(apply(X,apply(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,apply(k,Z)),apply(Y,Z)),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
apply(apply(apply(abstraction,X0),X1),X2) = apply(apply(X0,apply(k,X2)),apply(X1,X2)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t18,plain,
apply(apply(X1,apply(k,X2)),apply(X3,X2)) = apply(apply(apply(abstraction,X1),X3),X2),
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t31,plain,
apply(apply(X1,apply(k,X2)),apply(X3,X2)) = apply(apply(apply(abstraction,X1),X3),X2),
inference(orient,[status(thm)],[t18]) ).
cnf(f0,axiom,
apply(apply(k,X),Y) = X,
file('/export/starexec/sandbox/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(t6,plain,
apply(apply(k,X1),X2) = X1,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t20,plain,
apply(apply(k,X1),X2) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t35,plain,
apply(apply(apply(abstraction,X1),apply(k,X2)),X3) = apply(apply(X1,apply(k,X3)),X2),
inference(cp,[status(thm)],[t31,t20]) ).
cnf(t518,plain,
apply(apply(apply(abstraction,X1),apply(k,X2)),X3) = apply(apply(X1,apply(k,X3)),X2),
inference(orient,[status(thm)],[t35]) ).
cnf(t520,plain,
apply(apply(apply(k,X1),apply(k,X2)),X1) = apply(apply(apply(apply(abstraction,abstraction),k),X1),X2),
inference(cp,[status(thm)],[t518,t31]) ).
cnf(t617,plain,
apply(X1,X1) = apply(apply(apply(apply(abstraction,abstraction),k),X1),X2),
inference(step,[status(thm)],[t520,t20]) ).
cnf(t532,plain,
apply(X1,X1) = apply(apply(apply(apply(abstraction,abstraction),k),X1),X2),
inference(orient,[status(thm)],[t617]) ).
cnf(t588,plain,
false = eqq(apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k))),apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k)))),
inference(cp,[status(thm)],[t65,t532]) ).
cnf(t0,plain,
eqq(X1,X1) = true,
introduced(definition) ).
cnf(t56,plain,
eqq(X1,X1) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t618,plain,
false = true,
inference(step,[status(thm)],[t588,t56]) ).
cnf(t592,plain,
false = true,
inference(orient,[status(thm)],[t618]) ).
cnf(f9,axiom,
projection1 != projection2,
file('/export/starexec/sandbox/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(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c9,c10]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t592]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL075-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/5.37 % Computer : n003.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Fri Sep 25 07:30:58 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.83/6.89 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.83/6.89 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------