%------------------------------------------------------------------------------
% File : SPASS-SCL---0.1.1
% Problem : LCL398-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : /export/starexec/sandbox/solver/bin/SPASS-SCL-FOL -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 01:09:28 PM UTC 2026
% Result : Unsatisfiable 16.35s 16.65s
% Output : Proof 16.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 6 unt; 0 nHn; 4 RR)
% Number of literals : 13 ( 0 equ; 5 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 13 ( 2 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_3,axiom,
is_a_theorem(implies(X0,implies(not(X0),X1))),
file('theBenchmark.p',cn_3) ).
% CNF SPASS RESOLUTION.
cnf(c_9,plain,
( ~ is_a_theorem(X0)
| is_a_theorem(implies(not(X0),X1)) ),
inference(resolution,[status(thm)],[condensed_detachment,cn_3]) ).
% FILE RECORD
cnf(prove_cn_64,negated_conjecture,
~ is_a_theorem(implies(not(implies(x,x)),y)),
file('theBenchmark.p',prove_cn_64) ).
% FILE RECORD
cnf(cn_1,axiom,
is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
file('theBenchmark.p',cn_1) ).
% FILE RECORD
cnf(cn_2,axiom,
is_a_theorem(implies(implies(not(X0),X0),X0)),
file('theBenchmark.p',cn_2) ).
% CNF SPASS RESOLUTION.
cnf(c_6,plain,
( ~ is_a_theorem(implies(X0,implies(not(X1),X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[condensed_detachment,cn_1,condensed_detachment,cn_2]) ).
% CNF SPASS RESOLUTION.
cnf(c_8,plain,
is_a_theorem(implies(X0,X0)),
inference(resolution,[status(thm)],[c_6,cn_3]) ).
% CNF SPASS RESOLUTION.
cnf(c_10,plain,
$false,
inference(resolution,[status(thm)],[c_9,prove_cn_64,c_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL398-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/SPASS-SCL-FOL -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n013.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 4 17:53:19 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 Running /export/starexec/sandbox/solver/bin/SPASS-SCL-FOL -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.35/16.65
% 16.35/16.65 % Input Clauses:
% 16.35/16.65 % 1:3:2:INP:TopTop: is_a_theorem(implies(x0,x1)),is_a_theorem(x0) -> is_a_theorem(x1)
% 16.35/16.65 % 2:1:3:INP:TopTopTop: -> is_a_theorem(implies(implies(x0,x1),implies(implies(x1,x2),implies(x0,x2))))
% 16.35/16.65 % 3:1:1:INP:Top: -> is_a_theorem(implies(implies(not(x0),x0),x0))
% 16.35/16.65 % 4:1:2:INP:TopTop: -> is_a_theorem(implies(x0,implies(not(x0),x1)))
% 16.35/16.65 % 5:1:0:INP:: is_a_theorem(implies(not(implies(x,x)),y)) ->
% 16.35/16.65
% 16.35/16.65 % Predicates: is_a_theorem
% 16.35/16.65 % Fol Constants: x y
% 16.35/16.65 % Fol Functions: implies not
% 16.35/16.65 % Problem Properties:
% 16.35/16.65 % This is a full first-order problem without equality. The Problem is non-linear.
% 16.35/16.65
% 16.35/16.65
% 16.35/16.65 % Reduced Input Axiom Clauses:
% 16.35/16.65 % 1:3:2:INP:TopTop: is_a_theorem(implies(x0,x1)),is_a_theorem(x0) -> is_a_theorem(x1)
% 16.35/16.65 % 2:1:3:INP:TopTopTop: -> is_a_theorem(implies(implies(x0,x1),implies(implies(x1,x2),implies(x0,x2))))
% 16.35/16.65 % 3:1:1:INP:Top: -> is_a_theorem(implies(implies(not(x0),x0),x0))
% 16.35/16.65 % 4:1:2:INP:TopTop: -> is_a_theorem(implies(x0,implies(not(x0),x1)))
% 16.35/16.65
% 16.35/16.65 % Reduced Input Conjecture Clauses:
% 16.35/16.65 % 5:1:0:INP:: is_a_theorem(implies(not(implies(x,x)),y)) ->
% 16.35/16.65
% 16.35/16.65
% 16.35/16.65 % === Starting SPASS-SCL-FOL A Little Less Naive, considering 86 atoms initially. Used heuristic: lcl ===
% 16.35/16.65
% 16.35/16.65
% 16.35/16.65
% 16.35/16.65 % SZS status Unsatisfiable
% 16.35/16.65 % Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.35/16.65
% 16.35/16.65 % SPASS-SCL-FOL Statistics:
% 16.35/16.65 % Number of learned clauses: 4
% 16.35/16.65 % Number of propagations: 635
% 16.35/16.65 % Number of decisions: 153
% 16.35/16.65 % Number of resolutions: 8
% 16.35/16.65 % Number of condensations: 0
% 16.35/16.65 % Number of sub resolutions: 0
% 16.35/16.65
% 16.35/16.65 % Solver is done. Empty clause found
% 16.35/16.65
% 16.35/16.65 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 16.35/16.65 % SZS output start Proof for theBenchmark
% See solution above
% 16.35/16.65 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 16.35/16.65
% 16.35/16.65
% 16.35/16.65 % Needed: 0:0:16.30
% 16.35/16.65
% 16.35/16.65 % ###
% 16.35/16.65 % ### Pagesize: 8192
% 16.35/16.65 % ### Marksize: 0
% 16.35/16.65 % ### Memory demanded: 27196 KBytes
% 16.35/16.65 % ### Memory freed: 27196 KBytes
% 16.35/16.65 % ### Memory remaining: 0 Bytes
% 16.35/16.65 % ### Pages allocated: 3295 Pages
% 16.35/16.65 % ###
%------------------------------------------------------------------------------