%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COL006-2 : TPTP v9.2.1. Released v1.0.0.
% 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 : n023.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 04:12:01 PM UTC 2026
% Result : Unsatisfiable 58.07s 33.74s
% Output : CNFRefutation 58.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of clauses : 24 ( 22 unt; 0 nHn; 9 RR)
% Number of literals : 26 ( 21 equ; 8 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 43 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(k_definition,axiom,
apply(apply(k,X1),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_definition) ).
cnf(s_definition,axiom,
apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_definition) ).
cnf(prove_strong_fixed_point,negated_conjecture,
~ fixed_point(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
cnf(strong_fixed_point,axiom,
( fixed_point(X1)
| apply(X1,fixed_pt) != apply(fixed_pt,apply(X1,fixed_pt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',strong_fixed_point) ).
cnf(c_0_4,axiom,
apply(apply(k,X1),X2) = X1,
k_definition ).
cnf(c_0_5,axiom,
apply(apply(apply(s,X1),X2),X3) = apply(apply(X1,X3),apply(X2,X3)),
s_definition ).
cnf(c_0_6,plain,
apply(apply(apply(s,k),X1),X2) = X2,
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_7,plain,
apply(apply(apply(s,apply(s,k)),X1),X2) = apply(X1,X2),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,negated_conjecture,
~ fixed_point(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k)))),
prove_strong_fixed_point ).
cnf(c_0_9,axiom,
( fixed_point(X1)
| apply(X1,fixed_pt) != apply(fixed_pt,apply(X1,fixed_pt)) ),
strong_fixed_point ).
cnf(c_0_10,plain,
apply(apply(apply(s,apply(apply(s,k),X1)),X2),X3) = apply(X3,apply(X2,X3)),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_11,plain,
apply(apply(apply(s,apply(s,apply(s,k))),X1),X2) = apply(X2,apply(X1,X2)),
inference(spm,[status(thm)],[c_0_5,c_0_7]) ).
cnf(c_0_12,plain,
apply(apply(apply(s,apply(k,X1)),X2),X3) = apply(X1,apply(X2,X3)),
inference(spm,[status(thm)],[c_0_5,c_0_4]) ).
cnf(c_0_13,negated_conjecture,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt))))) != apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_5]),c_0_4]),c_0_5]),c_0_4]),c_0_5]),c_0_4]),c_0_5]),c_0_4]),c_0_5]),c_0_4]),c_0_5]),c_0_4]) ).
cnf(c_0_14,plain,
apply(apply(apply(s,apply(apply(s,k),X1)),X2),X3) = apply(apply(apply(s,apply(s,apply(s,k))),X2),X3),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
apply(apply(apply(s,apply(s,apply(k,X1))),X2),X3) = apply(X1,apply(X3,apply(X2,X3))),
inference(spm,[status(thm)],[c_0_5,c_0_12]) ).
cnf(c_0_16,negated_conjecture,
apply(fixed_pt,apply(apply(apply(s,apply(s,apply(s,k))),apply(apply(s,k),k)),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt))))) != apply(apply(apply(s,apply(s,apply(s,k))),apply(apply(s,k),k)),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14]),c_0_14]) ).
cnf(c_0_17,plain,
apply(X1,apply(apply(apply(s,apply(s,apply(s,k))),X2),X3)) = apply(apply(apply(s,apply(s,apply(k,X1))),X2),X3),
inference(spm,[status(thm)],[c_0_15,c_0_11]) ).
cnf(c_0_18,plain,
apply(apply(apply(s,X1),apply(apply(s,k),X2)),X3) = apply(apply(X1,X3),X3),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_19,negated_conjecture,
apply(apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),k)),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt)))) != apply(apply(apply(s,apply(s,apply(s,k))),apply(apply(s,k),k)),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt)))),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
apply(apply(apply(s,X1),apply(apply(s,k),X2)),X3) = apply(apply(apply(s,X1),apply(apply(s,k),X4)),X3),
inference(spm,[status(thm)],[c_0_18,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
apply(apply(apply(s,apply(s,apply(k,fixed_pt))),apply(apply(s,k),X1)),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt)))) != apply(apply(apply(s,apply(s,apply(s,k))),apply(apply(s,k),k)),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt)))),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,plain,
apply(apply(apply(s,apply(s,apply(s,k))),apply(apply(s,k),X1)),X2) = apply(X2,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_6]),c_0_14]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_5]),c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL006-2 : TPTP v9.2.1. Released v1.0.0.
% 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
% 0.16/0.33 % Computer : n023.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 16:14:08 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 58.07/33.74 % Version : CSE_E---1.7
% 58.07/33.74 % Problem : theBenchmark.p
% 58.07/33.74 % SZS status Unsatisfiable for theBenchmark.p
% 58.07/33.74 % SZS output start CNFRefutation
% See solution above
% 58.27/33.96 % Total time : 25.420s
%------------------------------------------------------------------------------