%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COL009-1 : TPTP v9.2.1. Released v1.0.0.
% 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 : n026.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 04:12:02 PM UTC 2026
% Result : Unsatisfiable 1.99s 1.91s
% Output : CNFRefutation 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of clauses : 19 ( 19 unt; 0 nHn; 7 RR)
% Number of literals : 19 ( 18 equ; 6 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(b_definition,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).
cnf(l2_definition,axiom,
apply(apply(l2,X1),X2) = apply(X2,apply(X1,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_definition) ).
cnf(prove_fixed_point,negated_conjecture,
X1 != apply(combinator,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_fixed_point) ).
cnf(c_0_3,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
b_definition ).
cnf(c_0_4,axiom,
apply(apply(l2,X1),X2) = apply(X2,apply(X1,X1)),
l2_definition ).
cnf(c_0_5,negated_conjecture,
X1 != apply(combinator,X1),
prove_fixed_point ).
cnf(c_0_6,plain,
apply(apply(apply(l2,X1),apply(b,X2)),X3) = apply(X2,apply(apply(X1,X1),X3)),
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_7,negated_conjecture,
apply(apply(apply(l2,X1),apply(b,combinator)),X2) != apply(apply(X1,X1),X2),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,plain,
apply(apply(l2,X1),apply(l2,X2)) = apply(apply(X1,X1),apply(X2,X2)),
inference(spm,[status(thm)],[c_0_4,c_0_4]) ).
cnf(c_0_9,negated_conjecture,
apply(apply(apply(l2,X1),apply(b,combinator)),apply(X2,X2)) != apply(apply(l2,X1),apply(l2,X2)),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_10,plain,
apply(apply(l2,l2),apply(l2,X1)) = apply(apply(X1,X1),apply(l2,l2)),
inference(spm,[status(thm)],[c_0_4,c_0_8]) ).
cnf(c_0_11,plain,
apply(apply(l2,X1),apply(apply(b,X2),X3)) = apply(X2,apply(X3,apply(X1,X1))),
inference(spm,[status(thm)],[c_0_4,c_0_3]) ).
cnf(c_0_12,negated_conjecture,
apply(apply(l2,X1),apply(apply(l2,X2),apply(b,combinator))) != apply(apply(l2,X2),apply(l2,X1)),
inference(spm,[status(thm)],[c_0_9,c_0_4]) ).
cnf(c_0_13,plain,
apply(apply(l2,l2),apply(apply(l2,X1),apply(b,X2))) = apply(X2,apply(apply(l2,l2),apply(l2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_10]),c_0_4]) ).
cnf(c_0_14,plain,
apply(apply(l2,X1),apply(apply(b,X2),X3)) = apply(X2,apply(apply(l2,X1),X3)),
inference(spm,[status(thm)],[c_0_11,c_0_4]) ).
cnf(c_0_15,plain,
apply(X1,apply(X2,apply(X3,apply(apply(b,X2),X3)))) = apply(apply(l2,apply(apply(b,X2),X3)),X1),
inference(spm,[status(thm)],[c_0_4,c_0_3]) ).
cnf(c_0_16,negated_conjecture,
apply(combinator,apply(apply(l2,l2),apply(l2,X1))) != apply(apply(l2,X1),apply(l2,l2)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
apply(X1,apply(apply(l2,X2),apply(X3,apply(apply(b,apply(b,X1)),X3)))) = apply(apply(l2,apply(apply(b,apply(b,X1)),X3)),apply(l2,X2)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_16,c_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL009-1 : TPTP v9.2.1. Released v1.0.0.
% 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
% 0.15/0.32 % Computer : n026.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 16:14:23 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.99/1.91 % Version : CSE_E---1.7
% 1.99/1.91 % Problem : theBenchmark.p
% 1.99/1.91 % SZS status Unsatisfiable for theBenchmark.p
% 1.99/1.91 % SZS output start CNFRefutation
% See solution above
% 1.99/1.92 % Total time : 1.370s
%------------------------------------------------------------------------------