%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COL078-2 : TPTP v9.2.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:12:16 PM UTC 2026
% Result : Unsatisfiable 1.29s 1.73s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of clauses : 27 ( 20 unt; 0 nHn; 12 RR)
% Number of literals : 34 ( 33 equ; 10 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 41 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(extensionality2,axiom,
( X1 = X2
| apply(X1,n(X1,X2)) != apply(X2,n(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality2) ).
cnf(k_definition,axiom,
apply(k(X1),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).
cnf(abstraction,axiom,
apply(apply(apply(abstraction,X1),X2),X3) = apply(apply(X1,k(X3)),apply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstraction) ).
cnf(identity_definition,axiom,
apply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_definition) ).
cnf(prove_TRC1b,negated_conjecture,
apply(apply(apply(abstraction,abstraction),abstraction),abstraction) != k(k(identity)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_TRC1b) ).
cnf(c_0_5,axiom,
( X1 = X2
| apply(X1,n(X1,X2)) != apply(X2,n(X1,X2)) ),
extensionality2 ).
cnf(c_0_6,axiom,
apply(k(X1),X2) = X1,
k_definition ).
cnf(c_0_7,axiom,
apply(apply(apply(abstraction,X1),X2),X3) = apply(apply(X1,k(X3)),apply(X2,X3)),
abstraction ).
cnf(c_0_8,plain,
( k(X1) = X2
| apply(X2,n(k(X1),X2)) != X1 ),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_9,plain,
apply(apply(apply(abstraction,k(X1)),X2),X3) = apply(X1,apply(X2,X3)),
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_10,plain,
( k(X1) = apply(apply(abstraction,k(X2)),X3)
| apply(X2,apply(X3,n(k(X1),apply(apply(abstraction,k(X2)),X3)))) != X1 ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_11,plain,
apply(apply(abstraction,k(k(X1))),X2) = k(X1),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_6])]) ).
cnf(c_0_12,axiom,
apply(identity,X1) = X1,
identity_definition ).
cnf(c_0_13,plain,
apply(abstraction,k(k(X1))) = k(k(X1)),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_11])]) ).
cnf(c_0_14,plain,
( X1 = identity
| apply(X1,n(X1,identity)) != n(X1,identity) ),
inference(spm,[status(thm)],[c_0_5,c_0_12]) ).
cnf(c_0_15,plain,
apply(apply(apply(abstraction,identity),X1),X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_12]),c_0_6]) ).
cnf(c_0_16,plain,
apply(apply(apply(abstraction,abstraction),X1),k(X2)) = k(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_13]),c_0_6]) ).
cnf(c_0_17,plain,
apply(apply(abstraction,identity),X1) = identity,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
( identity = X1
| apply(X1,n(identity,X1)) != n(identity,X1) ),
inference(spm,[status(thm)],[c_0_5,c_0_12]) ).
cnf(c_0_19,plain,
apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),X1)),X2),X3) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_16]),c_0_6]) ).
cnf(c_0_20,plain,
( apply(abstraction,identity) = X1
| apply(X1,n(apply(abstraction,identity),X1)) != identity ),
inference(spm,[status(thm)],[c_0_5,c_0_17]) ).
cnf(c_0_21,plain,
apply(apply(abstraction,apply(apply(abstraction,abstraction),X1)),X2) = identity,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,negated_conjecture,
apply(apply(apply(abstraction,abstraction),abstraction),abstraction) != k(k(identity)),
prove_TRC1b ).
cnf(c_0_23,plain,
k(identity) = apply(abstraction,identity),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_6])]) ).
cnf(c_0_24,plain,
apply(abstraction,apply(apply(abstraction,abstraction),X1)) = apply(abstraction,identity),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
apply(apply(apply(abstraction,abstraction),abstraction),abstraction) != k(apply(abstraction,identity)),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,plain,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_24]),c_0_7])]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL078-2 : TPTP v9.2.1. Released v1.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n013.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 16:15:56 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.29/1.73 % Version : CSE_E---1.7
% 1.29/1.73 % Problem : theBenchmark.p
% 1.29/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 1.29/1.73 % SZS output start CNFRefutation
% See solution above
% 1.29/1.74 % Total time : 1.373s
%------------------------------------------------------------------------------