%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COL042-6 : TPTP v9.2.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n008.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 04:12:06 PM UTC 2026
% Result : Unsatisfiable 6.59s 4.61s
% Output : CNFRefutation 6.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of clauses : 16 ( 16 unt; 0 nHn; 5 RR)
% Number of literals : 16 ( 15 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(w1_definition,axiom,
apply(apply(w1,X1),X2) = apply(apply(X2,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w1_definition) ).
cnf(b_definition,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).
cnf(strong_fixed_point,axiom,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),b)),b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',strong_fixed_point) ).
cnf(prove_strong_fixed_point,negated_conjecture,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
cnf(c_0_4,axiom,
apply(apply(w1,X1),X2) = apply(apply(X2,X1),X1),
w1_definition ).
cnf(c_0_5,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
b_definition ).
cnf(c_0_6,plain,
apply(apply(w1,X1),apply(apply(b,X2),X3)) = apply(apply(X2,apply(X3,X1)),X1),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_7,plain,
apply(apply(w1,X1),apply(apply(b,apply(b,X2)),X3)) = apply(X2,apply(apply(X3,X1),X1)),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,axiom,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),b)),b),
strong_fixed_point ).
cnf(c_0_9,plain,
apply(apply(w1,X1),apply(apply(b,apply(b,X2)),X3)) = apply(X2,apply(apply(w1,X1),X3)),
inference(spm,[status(thm)],[c_0_7,c_0_4]) ).
cnf(c_0_10,plain,
apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,X1)))) = apply(strong_fixed_point,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_8]),c_0_5]),c_0_5]) ).
cnf(c_0_11,plain,
apply(X1,apply(apply(w1,apply(apply(b,apply(b,X1)),X2)),X2)) = apply(apply(w1,apply(apply(b,apply(b,X1)),X2)),w1),
inference(spm,[status(thm)],[c_0_4,c_0_9]) ).
cnf(c_0_12,plain,
apply(apply(w1,apply(apply(b,apply(b,X1)),w1)),w1) = apply(strong_fixed_point,X1),
inference(rw,[status(thm)],[c_0_10,c_0_6]) ).
cnf(c_0_13,negated_conjecture,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
prove_strong_fixed_point ).
cnf(c_0_14,plain,
apply(X1,apply(strong_fixed_point,X1)) = apply(strong_fixed_point,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_12]) ).
cnf(c_0_15,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL042-6 : TPTP v9.2.1. Released v2.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n008.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 16:14:43 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 6.59/4.61 % Version : CSE_E---1.7
% 6.59/4.61 % Problem : theBenchmark.p
% 6.59/4.61 % SZS status Unsatisfiable for theBenchmark.p
% 6.59/4.61 % SZS output start CNFRefutation
% See solution above
% 6.59/4.63 % Total time : 3.369s
%------------------------------------------------------------------------------