%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COL043-3 : TPTP v9.2.1. Bugfixed v2.3.0.
% 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 04:12:07 PM UTC 2026
% Result : Unsatisfiable 31.72s 18.96s
% Output : CNFRefutation 31.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of clauses : 18 ( 18 unt; 0 nHn; 5 RR)
% Number of literals : 18 ( 17 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 11 ( 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 : 31 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(h_definition,axiom,
apply(apply(apply(h,X1),X2),X3) = apply(apply(apply(X1,X2),X3),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_definition) ).
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(strong_fixed_point,axiom,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b)),b),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
cnf(c_0_4,axiom,
apply(apply(apply(h,X1),X2),X3) = apply(apply(apply(X1,X2),X3),X2),
h_definition ).
cnf(c_0_5,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
b_definition ).
cnf(c_0_6,axiom,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(apply(h,apply(apply(b,apply(apply(b,h),apply(b,b))),apply(h,apply(apply(b,h),apply(b,b))))),h)),b)),b),
strong_fixed_point ).
cnf(c_0_7,plain,
apply(apply(apply(h,apply(apply(b,X1),X2)),X3),X4) = apply(apply(apply(X1,apply(X2,X3)),X4),X3),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_8,plain,
apply(apply(apply(h,apply(apply(b,b),apply(apply(h,apply(apply(b,h),apply(b,b))),h))),apply(b,apply(b,X1))),h) = apply(strong_fixed_point,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6]),c_0_5]),c_0_7]),c_0_5]) ).
cnf(c_0_9,plain,
apply(apply(apply(h,apply(apply(b,b),X1)),X2),X3) = apply(apply(X1,X2),apply(X3,X2)),
inference(spm,[status(thm)],[c_0_5,c_0_7]) ).
cnf(c_0_10,plain,
apply(apply(apply(h,apply(b,X1)),X2),X3) = apply(apply(X1,apply(X2,X3)),X2),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_11,plain,
apply(apply(apply(apply(h,apply(apply(b,b),h)),apply(b,apply(b,X1))),h),apply(h,apply(b,apply(b,X1)))) = apply(strong_fixed_point,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_7]) ).
cnf(c_0_12,plain,
apply(apply(apply(h,apply(b,apply(b,X1))),X2),X3) = apply(X1,apply(apply(X2,X3),X2)),
inference(spm,[status(thm)],[c_0_5,c_0_10]) ).
cnf(c_0_13,plain,
apply(apply(apply(h,apply(b,apply(b,X1))),apply(h,apply(b,apply(b,X1)))),apply(h,apply(b,apply(b,X1)))) = apply(strong_fixed_point,X1),
inference(spm,[status(thm)],[c_0_11,c_0_9]) ).
cnf(c_0_14,plain,
apply(apply(apply(h,apply(b,apply(b,X1))),apply(h,apply(b,apply(b,X2)))),apply(h,apply(b,apply(b,X2)))) = apply(X1,apply(strong_fixed_point,X2)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,negated_conjecture,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
prove_strong_fixed_point ).
cnf(c_0_16,plain,
apply(X1,apply(strong_fixed_point,X1)) = apply(strong_fixed_point,X1),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL043-3 : TPTP v9.2.1. Bugfixed v2.3.0.
% 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 : n026.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 16:15:53 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 31.72/18.96 % Version : CSE_E---1.7
% 31.72/18.96 % Problem : theBenchmark.p
% 31.72/18.96 % SZS status Unsatisfiable for theBenchmark.p
% 31.72/18.96 % SZS output start CNFRefutation
% See solution above
% 31.85/19.07 % Total time : 14.395s
%------------------------------------------------------------------------------