%------------------------------------------------------------------------------
% File : SPASS-SCL---0.1.1
% Problem : LCL678+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : /export/starexec/sandbox/solver/bin/SPASS-SCL-FOL -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 01:10:09 PM UTC 2026
% Result : Theorem 0.13s 0.36s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 7 unt; 1 def)
% Number of atoms : 62 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 88 ( 46 ~; 35 |; 6 &)
% ( 0 <=>; 0 =>; 1 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 48 ( 6 sgn 29 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
% FILE RECORD
fof(main,conjecture,
~ ? [X1] :
~ ( $false
| ~ ! [X2] :
( ~ r1(X1,X2)
| $false
| ~ ! [X1] :
( ~ r1(X2,X1)
| ! [X2] :
( ~ r1(X1,X2)
| p1(X2) )
| ~ ! [X2] :
( ~ r1(X1,X2)
| p1(X2) ) ) ) ),
file('theBenchmark.p',main) ).
% NEGATING CONJECTURE
fof(main_nc,negated_conjecture,
? [X1] :
~ ( $false
| ~ ! [X2] :
( ~ r1(X1,X2)
| $false
| ~ ! [X1] :
( ~ r1(X2,X1)
| ! [X2] :
( ~ r1(X1,X2)
| p1(X2) )
| ~ ! [X2] :
( ~ r1(X1,X2)
| p1(X2) ) ) ) ),
inference(negating_conjecture,[status(cth)],[main]) ).
% FOF SIMPLE INFERENCE
fof(main_nc_elimTB,negated_conjecture,
? [X1] :
~ ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ! [X3] :
( ~ r1(X2,X3)
| ! [X4] :
( ~ r1(X3,X4)
| p1(X4) )
| ~ ! [X5] :
( ~ r1(X3,X5)
| p1(X5) ) ) ),
inference(elimTB,[status(thm)],[inference(variable_rename,[status(thm)],[main_nc])]) ).
% FOF INTRODUCE RENAMING
fof(ren1_defn,definition,
! [X2,X3] :
( ren1(X2,X3)
<= ( ~ r1(X2,X3)
| ! [X4] :
( ~ r1(X3,X4)
| p1(X4) )
| ~ ! [X5] :
( ~ r1(X3,X5)
| p1(X5) ) ) ),
introduced(definition,[new_symbols(definition,[ren1])],[main_nc_elimTB]) ).
% FOF SIMPLE INFERENCE
fof(ren1_elimImpEquivPushNegMiniScope,plain,
! [X1,X2] :
( ( r1(X1,X2)
& ? [X3] :
( r1(X2,X3)
& ~ p1(X3) )
& ! [X4] :
( ~ r1(X2,X4)
| p1(X4) ) )
| ren1(X1,X2) ),
inference(elimImpEquivPushNegMiniScope,[status(thm)],[ren1_defn]) ).
% FOF SKOLEM INFERENCE. WIP!!
fof(ren1_skol,plain,
! [X1,X2] :
( ( r1(X1,X2)
& r1(X2,skf1(X2))
& ~ p1(skf1(X2))
& ! [X4] :
( ~ r1(X2,X4)
| p1(X4) ) )
| ren1(X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[skf1]),skolemize(X3,skf1(X2))],[ren1_elimImpEquivPushNegMiniScope]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_6,plain,
( ~ r1(X0,X1)
| p1(X1)
| ren1(X2,X0) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[ren1_skol])]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_4,plain,
( r1(X0,skf1(X0))
| ren1(X1,X0) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[ren1_skol])]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_5,plain,
( ~ p1(skf1(X0))
| ren1(X1,X0) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[ren1_skol])]) ).
% CNF SPASS RESOLUTION.
cnf(c_8,plain,
ren1(X0,X1),
inference(resolution,[status(thm)],[c_6,c_4,c_5]) ).
% FOF RENAMING INFERENCE
fof(main_nc_renObv,negated_conjecture,
? [X1] :
~ ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ! [X3] : ren1(X2,X3) ),
inference(renaming,[status(esa)],[main_nc_elimTB,ren1_defn]) ).
% FOF SIMPLE INFERENCE
fof(main_nc_elimImpEquivPushNegMiniScope,negated_conjecture,
? [X1] :
! [X2] :
( ~ r1(X1,X2)
| ? [X3] : ~ ren1(X2,X3) ),
inference(elimImpEquivPushNegMiniScope,[status(thm)],[main_nc_renObv]) ).
% FOF SKOLEM INFERENCE. WIP!!
fof(main_nc_skol,negated_conjecture,
! [X2] :
( ~ r1(skc2,X2)
| ~ ren1(X2,skf3(X2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[skc2,skf3]),skolemize(X1,skc2),skolemize(X3,skf3(X2))],[main_nc_elimImpEquivPushNegMiniScope]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_7,plain,
( ~ r1(skc2,X0)
| ~ ren1(X0,skf3(X0)) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[main_nc_skol])]) ).
% CNF SPASS RESOLUTION.
cnf(c_9,plain,
~ r1(skc2,X0),
inference(resolution,[status(thm)],[c_8,c_7]) ).
% 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])]) ).
% CNF SPASS RESOLUTION.
cnf(c_10,plain,
$false,
inference(resolution,[status(thm)],[c_9,c_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL678+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/SPASS-SCL-FOL -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n026.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 5 23:59:56 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running /export/starexec/sandbox/solver/bin/SPASS-SCL-FOL -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36
% 0.13/0.36 % Input Clauses:
% 0.13/0.36 % 1:1:1:INP:Top: -> r1(x0,x0)
% 0.13/0.36 % 2:3:3:INP:TopTopTop: r1(x0,x1),r1(x1,x2) -> r1(x0,x2)
% 0.13/0.36 % 3:2:2:INP:TopTop: -> r1(x0,x1),ren1(x0,x1)
% 0.13/0.36 % 4:2:2:INP:TopTop: -> r1(x0,skf1(x0)),ren1(x1,x0)
% 0.13/0.36 % 5:2:2:INP:TopTop: p1(skf1(x0)) -> ren1(x1,x0)
% 0.13/0.36 % 6:3:3:INP:TopTopTop: r1(x0,x1) -> p1(x1),ren1(x2,x0)
% 0.13/0.36 % 7:2:1:INP:Top: r1(skc2,x0),ren1(x0,skf3(x0)) ->
% 0.13/0.36
% 0.13/0.36 % Predicates: r1 p1 ren1
% 0.13/0.36 % Fol Constants: skc2
% 0.13/0.36 % Fol Functions: skf1 skf3
% 0.13/0.36 % Problem Properties:
% 0.13/0.36 % This is a full first-order problem without equality. The Problem is non-linear.
% 0.13/0.36
% 0.13/0.36
% 0.13/0.36 % Reduced Input Axiom Clauses:
% 0.13/0.36 % 1:1:1:INP:Top: -> r1(x0,x0)
% 0.13/0.36 % 2:3:3:INP:TopTopTop: r1(x0,x1),r1(x1,x2) -> r1(x0,x2)
% 0.13/0.36 % 3:2:2:INP:TopTop: -> r1(x0,x1),ren1(x0,x1)
% 0.13/0.36 % 4:2:2:INP:TopTop: -> r1(x0,skf1(x0)),ren1(x1,x0)
% 0.13/0.36 % 5:2:2:INP:TopTop: p1(skf1(x0)) -> ren1(x1,x0)
% 0.13/0.36 % 6:3:3:INP:TopTopTop: r1(x0,x1) -> p1(x1),ren1(x2,x0)
% 0.13/0.36
% 0.13/0.36 % Reduced Input Conjecture Clauses:
% 0.13/0.36 % 7:2:1:INP:Top: r1(skc2,x0),ren1(x0,skf3(x0)) ->
% 0.13/0.36
% 0.13/0.36
% 0.13/0.36 % === Starting SPASS-SCL-FOL A Little Less Naive, considering 9 atoms initially. Used heuristic: lmodel_grow ===
% 0.13/0.36
% 0.13/0.36
% 0.13/0.36
% 0.13/0.36 % SZS status Theorem
% 0.13/0.36 % Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36
% 0.13/0.36 % SPASS-SCL-FOL Statistics:
% 0.13/0.36 % Number of learned clauses: 2
% 0.13/0.36 % Number of propagations: 6
% 0.13/0.36 % Number of decisions: 4
% 0.13/0.36 % Number of resolutions: 4
% 0.13/0.36 % Number of condensations: 1
% 0.13/0.36 % Number of sub resolutions: 0
% 0.13/0.36
% 0.13/0.36 % Solver is done. Empty clause found
% 0.13/0.36
% 0.13/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36
% 0.13/0.36
% 0.13/0.36 % Needed: 0:00:00.00
% 0.13/0.36
% 0.13/0.36 % ###
% 0.13/0.36 % ### Pagesize: 8192
% 0.13/0.36 % ### Marksize: 0
% 0.13/0.36 % ### Memory demanded: 275 KBytes
% 0.13/0.36 % ### Memory freed: 275 KBytes
% 0.13/0.36 % ### Memory remaining: 0 Bytes
% 0.13/0.36 % ### Pages allocated: 105 Pages
% 0.13/0.36 % ###
%------------------------------------------------------------------------------