%------------------------------------------------------------------------------
% File : SPASS-SCL---0.1.1
% Problem : LCL007-1 : 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 : n002.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 01:08:47 PM UTC 2026
% Result : Unsatisfiable 0.79s 1.11s
% Output : Proof 0.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 4
% Syntax : Number of clauses : 6 ( 4 unt; 0 nHn; 4 RR)
% Number of literals : 9 ( 0 equ; 4 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; 3 con; 0-2 aty)
% Number of variables : 9 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
% FILE RECORD
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(equivalent(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
file('theBenchmark.p',condensed_detachment) ).
% FILE RECORD
cnf(ec_4,axiom,
is_a_theorem(equivalent(equivalent(X0,X1),equivalent(X1,X0))),
file('theBenchmark.p',ec_4) ).
% CNF SPASS RESOLUTION.
cnf(c_6,plain,
( ~ is_a_theorem(equivalent(X0,X1))
| is_a_theorem(equivalent(X1,X0)) ),
inference(resolution,[status(thm)],[condensed_detachment,ec_4]) ).
% FILE RECORD
cnf(ec_5,axiom,
is_a_theorem(equivalent(equivalent(equivalent(X0,X1),X2),equivalent(X0,equivalent(X1,X2)))),
file('theBenchmark.p',ec_5) ).
% FILE RECORD
cnf(prove_ec_2,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(a,b),c))),
file('theBenchmark.p',prove_ec_2) ).
% CNF SPASS RESOLUTION.
cnf(c_10,plain,
$false,
inference(resolution,[status(thm)],[c_6,ec_5,prove_ec_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL007-1 : 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
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 4 17:54:05 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running /export/starexec/sandbox2/solver/bin/SPASS-SCL-FOL -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.79/1.11
% 0.79/1.11 % Input Clauses:
% 0.79/1.11 % 1:3:2:INP:TopTop: is_a_theorem(equivalent(x0,x1)),is_a_theorem(x0) -> is_a_theorem(x1)
% 0.79/1.11 % 2:1:2:INP:TopTop: -> is_a_theorem(equivalent(equivalent(x0,x1),equivalent(x1,x0)))
% 0.79/1.11 % 3:1:3:INP:TopTopTop: -> is_a_theorem(equivalent(equivalent(equivalent(x0,x1),x2),equivalent(x0,equivalent(x1,x2))))
% 0.79/1.11 % 4:1:0:INP:: is_a_theorem(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(a,b),c))) ->
% 0.79/1.11
% 0.79/1.11 % Predicates: is_a_theorem
% 0.79/1.11 % Fol Constants: a b c
% 0.79/1.11 % Fol Functions: equivalent
% 0.79/1.11 % Problem Properties:
% 0.79/1.11 % This is a full first-order problem without equality. The Problem is non-linear.
% 0.79/1.11
% 0.79/1.11
% 0.79/1.11 % Reduced Input Axiom Clauses:
% 0.79/1.11 % 1:3:2:INP:TopTop: is_a_theorem(equivalent(x0,x1)),is_a_theorem(x0) -> is_a_theorem(x1)
% 0.79/1.11 % 2:1:2:INP:TopTop: -> is_a_theorem(equivalent(equivalent(x0,x1),equivalent(x1,x0)))
% 0.79/1.11 % 3:1:3:INP:TopTopTop: -> is_a_theorem(equivalent(equivalent(equivalent(x0,x1),x2),equivalent(x0,equivalent(x1,x2))))
% 0.79/1.11
% 0.79/1.11 % Reduced Input Conjecture Clauses:
% 0.79/1.11 % 4:1:0:INP:: is_a_theorem(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(a,b),c))) ->
% 0.79/1.11
% 0.79/1.11
% 0.79/1.11 % === Starting SPASS-SCL-FOL A Little Less Naive, considering 31 atoms initially. Used heuristic: lcl ===
% 0.79/1.11
% 0.79/1.11
% 0.79/1.11
% 0.79/1.11 % SZS status Unsatisfiable
% 0.79/1.11 % Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.79/1.11
% 0.79/1.11 % SPASS-SCL-FOL Statistics:
% 0.79/1.11 % Number of learned clauses: 5
% 0.79/1.11 % Number of propagations: 228
% 0.79/1.11 % Number of decisions: 121
% 0.79/1.11 % Number of resolutions: 9
% 0.79/1.11 % Number of condensations: 0
% 0.79/1.11 % Number of sub resolutions: 0
% 0.79/1.11
% 0.79/1.11 % Solver is done. Empty clause found
% 0.79/1.11
% 0.79/1.11 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.79/1.11 % SZS output start Proof for theBenchmark
% See solution above
% 0.79/1.11 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.79/1.11
% 0.79/1.11
% 0.79/1.11 % Needed: 0:00:00.76
% 0.79/1.11
% 0.79/1.11 % ###
% 0.79/1.11 % ### Pagesize: 8192
% 0.79/1.11 % ### Marksize: 0
% 0.79/1.11 % ### Memory demanded: 8270 KBytes
% 0.79/1.11 % ### Memory freed: 8270 KBytes
% 0.79/1.11 % ### Memory remaining: 0 Bytes
% 0.79/1.11 % ### Pages allocated: 1055 Pages
% 0.79/1.11 % ###
%------------------------------------------------------------------------------