%------------------------------------------------------------------------------
% File : SPASS-SCL---0.1.1
% Problem : LCL666+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : /export/starexec/sandbox2/solver/bin/SPASS-SCL-FOL -t 300 /export/starexec/sandbox2/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 01:10:03 PM UTC 2026
% Result : Theorem 0.14s 0.36s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 7 unt; 0 def)
% Number of atoms : 35 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 47 ( 25 ~; 12 |; 10 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 14 ( 0 sgn 8 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
% FILE RECORD
fof(main,conjecture,
~ ? [X1] :
~ ( ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ( p201(X2)
& p101(X2) ) )
| ~ ( p201(X1)
& p101(X1) ) ),
file('theBenchmark.p',main) ).
% NEGATING CONJECTURE
fof(main_nc,negated_conjecture,
? [X1] :
~ ( ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ( p201(X2)
& p101(X2) ) )
| ~ ( p201(X1)
& p101(X1) ) ),
inference(negating_conjecture,[status(cth)],[main]) ).
% FOF SIMPLE INFERENCE
fof(main_nc_elimTB,negated_conjecture,
? [X1] :
~ ( ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ( p201(X2)
& p101(X2) ) )
| ~ ( p201(X1)
& p101(X1) ) ),
inference(elimTB,[status(thm)],[inference(variable_rename,[status(thm)],[main_nc])]) ).
% FOF SIMPLE INFERENCE
fof(main_nc_elimImpEquivPushNegMiniScope,negated_conjecture,
? [X1] :
( ! [X2] :
( ~ r1(X1,X2)
| ~ p201(X2)
| ~ p101(X2) )
& p201(X1)
& p101(X1) ),
inference(elimImpEquivPushNegMiniScope,[status(thm)],[main_nc_elimTB]) ).
% FOF SKOLEM INFERENCE. WIP!!
fof(main_nc_skol,negated_conjecture,
( ! [X2] :
( ~ r1(skc1,X2)
| ~ p201(X2)
| ~ p101(X2) )
& p201(skc1)
& p101(skc1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[skc1]),skolemize(X1,skc1)],[main_nc_elimImpEquivPushNegMiniScope]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_2,plain,
( ~ r1(skc1,X0)
| ~ p201(X0)
| ~ p101(X0) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[main_nc_skol])]) ).
% FILE RECORD
fof(reflexivity,axiom,
! [X1] : r1(X1,X1),
file('theBenchmark.p',reflexivity) ).
% FOF SIMPLE INFERENCE
fof(reflexivity_elimTB,axiom,
! [X1] : r1(X1,X1),
inference(elimTB,[status(thm)],[inference(variable_rename,[status(thm)],[reflexivity])]) ).
% FOF SIMPLE INFERENCE
fof(reflexivity_elimImpEquivPushNegMiniScope,axiom,
! [X1] : r1(X1,X1),
inference(elimImpEquivPushNegMiniScope,[status(thm)],[reflexivity_elimTB]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_1,plain,
r1(X0,X0),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[reflexivity_elimImpEquivPushNegMiniScope])]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_3,plain,
p201(skc1),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[main_nc_skol])]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_4,plain,
p101(skc1),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[main_nc_skol])]) ).
% CNF SPASS RESOLUTION.
cnf(c_5,plain,
$false,
inference(resolution,[status(thm)],[c_2,c_1,c_3,c_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL666+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/SPASS-SCL-FOL -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.35 % Computer : n013.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Sat Sep 5 21:18:35 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running /export/starexec/sandbox2/solver/bin/SPASS-SCL-FOL -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.36
% 0.14/0.36 % Input Clauses:
% 0.14/0.36 % 1:1:1:INP:Top: -> r1(x0,x0)
% 0.14/0.36 % 2:3:1:INP:Top: r1(skc1,x0),p201(x0),p101(x0) ->
% 0.14/0.36 % 3:1:0:INP:: -> p201(skc1)
% 0.14/0.36 % 4:1:0:INP:: -> p101(skc1)
% 0.14/0.36
% 0.14/0.36 % Predicates: r1 p201 p101
% 0.14/0.36 % Fol Constants: skc1
% 0.14/0.36 % Fol Functions:
% 0.14/0.36 % Problem Properties:
% 0.14/0.36 % This is a Bernays Schoenfinkel problem. The Problem is non-linear.
% 0.14/0.36
% 0.14/0.36
% 0.14/0.36 % Reduced Input Axiom Clauses:
% 0.14/0.36 % 1:1:1:INP:Top: -> r1(x0,x0)
% 0.14/0.36
% 0.14/0.36 % Reduced Input Conjecture Clauses:
% 0.14/0.36 % 2:3:1:INP:Top: r1(skc1,x0),p201(x0),p101(x0) ->
% 0.14/0.36 % 3:1:0:INP:: -> p201(skc1)
% 0.14/0.36 % 4:1:0:INP:: -> p101(skc1)
% 0.14/0.36
% 0.14/0.36
% 0.14/0.36 % === Starting SPASS-SCL-FOL A Little Less Naive, considering 3 atoms initially. Used heuristic: lmodel_grow ===
% 0.14/0.36
% 0.14/0.36
% 0.14/0.36
% 0.14/0.36 % SZS status Theorem
% 0.14/0.36 % Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.36
% 0.14/0.36 % SPASS-SCL-FOL Statistics:
% 0.14/0.36 % Number of learned clauses: 0
% 0.14/0.36 % Number of propagations: 3
% 0.14/0.36 % Number of decisions: 0
% 0.14/0.36 % Number of resolutions: 3
% 0.14/0.36 % Number of condensations: 0
% 0.14/0.36 % Number of sub resolutions: 0
% 0.14/0.36
% 0.14/0.36 % Solver is done. Empty clause found
% 0.14/0.36
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.36
% 0.14/0.36
% 0.14/0.36 % Needed: 0:00:00.00
% 0.14/0.36
% 0.14/0.36 % ###
% 0.14/0.36 % ### Pagesize: 8192
% 0.14/0.36 % ### Marksize: 0
% 0.14/0.36 % ### Memory demanded: 222 KBytes
% 0.14/0.36 % ### Memory freed: 222 KBytes
% 0.14/0.36 % ### Memory remaining: 0 Bytes
% 0.14/0.36 % ### Pages allocated: 87 Pages
% 0.14/0.36 % ###
%------------------------------------------------------------------------------