%------------------------------------------------------------------------------
% File : SPASS-SCL---0.1.1
% Problem : LCL076-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : /export/starexec/sandbox2/solver/bin/SPASS-SCL-FOL -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 01:08:54 PM UTC 2026
% Result : Unsatisfiable 0.80s 1.08s
% Output : Proof 0.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 1
% Number of leaves : 4
% Syntax : Number of clauses : 5 ( 4 unt; 0 nHn; 3 RR)
% Number of literals : 7 ( 0 equ; 3 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 5 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
% FILE RECORD
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
file('theBenchmark.p',condensed_detachment) ).
% FILE RECORD
cnf(cn_49,axiom,
is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))),
file('theBenchmark.p',cn_49) ).
% FILE RECORD
cnf(extra_lemma,axiom,
is_a_theorem(implies(not(not(X0)),X0)),
file('theBenchmark.p',extra_lemma) ).
% FILE RECORD
cnf(prove_cn_40,negated_conjecture,
~ is_a_theorem(implies(a,not(not(a)))),
file('theBenchmark.p',prove_cn_40) ).
% CNF SPASS RESOLUTION.
cnf(c_12,plain,
$false,
inference(resolution,[status(thm)],[condensed_detachment,cn_49,extra_lemma,prove_cn_40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL076-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/SPASS-SCL-FOL -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 4 19:43:08 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 Running /export/starexec/sandbox2/solver/bin/SPASS-SCL-FOL -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.80/1.08
% 0.80/1.08 % Input Clauses:
% 0.80/1.08 % 1:3:2:INP:TopTop: is_a_theorem(implies(x0,x1)),is_a_theorem(x0) -> is_a_theorem(x1)
% 0.80/1.08 % 2:1:2:INP:TopTop: -> is_a_theorem(implies(x0,implies(x1,x0)))
% 0.80/1.08 % 3:1:3:INP:TopTopTop: -> is_a_theorem(implies(implies(x0,implies(x1,x2)),implies(implies(x0,x1),implies(x0,x2))))
% 0.80/1.08 % 4:1:2:INP:TopTop: -> is_a_theorem(implies(implies(not(x0),not(x1)),implies(x1,x0)))
% 0.80/1.08 % 5:1:1:INP:Top: -> is_a_theorem(implies(not(not(x0)),x0))
% 0.80/1.08 % 6:1:0:INP:: is_a_theorem(implies(a,not(not(a)))) ->
% 0.80/1.08
% 0.80/1.08 % Predicates: is_a_theorem
% 0.80/1.08 % Fol Constants: a
% 0.80/1.08 % Fol Functions: implies not
% 0.80/1.08 % Problem Properties:
% 0.80/1.08 % This is a full first-order problem without equality. The Problem is non-linear.
% 0.80/1.08
% 0.80/1.08
% 0.80/1.08 % Reduced Input Axiom Clauses:
% 0.80/1.08 % 1:3:2:INP:TopTop: is_a_theorem(implies(x0,x1)),is_a_theorem(x0) -> is_a_theorem(x1)
% 0.80/1.08 % 2:1:2:INP:TopTop: -> is_a_theorem(implies(x0,implies(x1,x0)))
% 0.80/1.08 % 3:1:3:INP:TopTopTop: -> is_a_theorem(implies(implies(x0,implies(x1,x2)),implies(implies(x0,x1),implies(x0,x2))))
% 0.80/1.08 % 4:1:2:INP:TopTop: -> is_a_theorem(implies(implies(not(x0),not(x1)),implies(x1,x0)))
% 0.80/1.08 % 5:1:1:INP:Top: -> is_a_theorem(implies(not(not(x0)),x0))
% 0.80/1.08
% 0.80/1.08 % Reduced Input Conjecture Clauses:
% 0.80/1.08 % 6:1:0:INP:: is_a_theorem(implies(a,not(not(a)))) ->
% 0.80/1.08
% 0.80/1.08
% 0.80/1.08 % === Starting SPASS-SCL-FOL A Little Less Naive, considering 80 atoms initially. Used heuristic: lcl ===
% 0.80/1.08
% 0.80/1.08
% 0.80/1.08
% 0.80/1.08 % SZS status Unsatisfiable
% 0.80/1.08 % Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.80/1.08
% 0.80/1.08 % SPASS-SCL-FOL Statistics:
% 0.80/1.08 % Number of learned clauses: 5
% 0.80/1.08 % Number of propagations: 269
% 0.80/1.08 % Number of decisions: 167
% 0.80/1.08 % Number of resolutions: 10
% 0.80/1.08 % Number of condensations: 0
% 0.80/1.08 % Number of sub resolutions: 0
% 0.80/1.08
% 0.80/1.08 % Solver is done. Empty clause found
% 0.80/1.08
% 0.80/1.08 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.80/1.08 % SZS output start Proof for theBenchmark
% See solution above
% 0.80/1.08 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.80/1.08
% 0.80/1.08
% 0.80/1.08 % Needed: 0:00:00.71
% 0.80/1.08
% 0.80/1.08 % ###
% 0.80/1.08 % ### Pagesize: 8192
% 0.80/1.08 % ### Marksize: 0
% 0.80/1.08 % ### Memory demanded: 35618 KBytes
% 0.80/1.08 % ### Memory freed: 35618 KBytes
% 0.80/1.08 % ### Memory remaining: 0 Bytes
% 0.80/1.08 % ### Pages allocated: 4343 Pages
% 0.80/1.08 % ###
%------------------------------------------------------------------------------