%------------------------------------------------------------------------------
% File : SPASS-SCL---0.1.1
% Problem : LCL686+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 : n006.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 01:10:15 PM UTC 2026
% Result : Theorem 0.13s 0.37s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 8 unt; 2 def)
% Number of atoms : 154 ( 0 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 231 ( 105 ~; 85 |; 39 &)
% ( 0 <=>; 0 =>; 2 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-1 aty)
% Number of variables : 64 ( 0 sgn 44 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
% FILE RECORD
fof(main,conjecture,
~ ? [X1] :
~ ( ! [X2] :
( ~ r1(X1,X2)
| ~ p3(X2)
| ! [X1] :
( ~ r1(X2,X1)
| ~ p1(X1) ) )
| ! [X2] :
( ~ r1(X1,X2)
| ~ ! [X1] :
( ~ r1(X2,X1)
| ~ ( ! [X2] :
( ~ r1(X1,X2)
| $false )
| ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ( ( p2(X2)
& ~ p1(X2) )
| ( ~ p2(X2)
& p1(X2) ) ) )
| ! [X2] :
( ~ r1(X1,X2)
| p3(X2) )
| ! [X2] :
( ~ r1(X1,X2)
| ( ~ p1(X2)
& ~ p2(X2) )
| ( p2(X2)
& p1(X2) ) ) ) ) ) ),
file('theBenchmark.p',main) ).
% NEGATING CONJECTURE
fof(main_nc,negated_conjecture,
? [X1] :
~ ( ! [X2] :
( ~ r1(X1,X2)
| ~ p3(X2)
| ! [X1] :
( ~ r1(X2,X1)
| ~ p1(X1) ) )
| ! [X2] :
( ~ r1(X1,X2)
| ~ ! [X1] :
( ~ r1(X2,X1)
| ~ ( ! [X2] :
( ~ r1(X1,X2)
| $false )
| ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ( ( p2(X2)
& ~ p1(X2) )
| ( ~ p2(X2)
& p1(X2) ) ) )
| ! [X2] :
( ~ r1(X1,X2)
| p3(X2) )
| ! [X2] :
( ~ r1(X1,X2)
| ( ~ p1(X2)
& ~ p2(X2) )
| ( p2(X2)
& p1(X2) ) ) ) ) ) ),
inference(negating_conjecture,[status(cth)],[main]) ).
% FOF SIMPLE INFERENCE
fof(main_nc_elimTB,negated_conjecture,
? [X1] :
~ ( ! [X2] :
( ~ r1(X1,X2)
| ~ p3(X2)
| ! [X3] :
( ~ r1(X2,X3)
| ~ p1(X3) ) )
| ! [X4] :
( ~ r1(X1,X4)
| ~ ! [X5] :
( ~ r1(X4,X5)
| ~ ( ! [X6] : ~ r1(X5,X6)
| ~ ! [X7] :
( ~ r1(X5,X7)
| ~ ( ( p2(X7)
& ~ p1(X7) )
| ( ~ p2(X7)
& p1(X7) ) ) )
| ! [X8] :
( ~ r1(X5,X8)
| p3(X8) )
| ! [X9] :
( ~ r1(X5,X9)
| ( ~ p1(X9)
& ~ p2(X9) )
| ( p2(X9)
& p1(X9) ) ) ) ) ) ),
inference(elimTB,[status(thm)],[inference(variable_rename,[status(thm)],[main_nc])]) ).
% FOF INTRODUCE RENAMING
fof(ren2_defn,definition,
! [X5] :
( ren2(X5)
<= ( ! [X6] : ~ r1(X5,X6)
| ~ ! [X7] :
( ~ r1(X5,X7)
| ~ ren1(X7) )
| ! [X8] :
( ~ r1(X5,X8)
| p3(X8) )
| ! [X9] :
( ~ r1(X5,X9)
| ( ~ p1(X9)
& ~ p2(X9) )
| ( p2(X9)
& p1(X9) ) ) ) ),
introduced(definition,[new_symbols(definition,[ren2])],[main_nc_elimTB]) ).
% FOF SIMPLE INFERENCE
fof(ren2_elimImpEquivPushNegMiniScope,plain,
! [X1] :
( ( ? [X2] : r1(X1,X2)
& ! [X3] :
( ~ r1(X1,X3)
| ~ ren1(X3) )
& ? [X4] :
( r1(X1,X4)
& ~ p3(X4) )
& ? [X5] :
( r1(X1,X5)
& ( p1(X5)
| p2(X5) )
& ( ~ p2(X5)
| ~ p1(X5) ) ) )
| ren2(X1) ),
inference(elimImpEquivPushNegMiniScope,[status(thm)],[ren2_defn]) ).
% FOF SKOLEM INFERENCE. WIP!!
fof(ren2_skol,plain,
! [X1] :
( ( r1(X1,skf1(X1))
& ! [X3] :
( ~ r1(X1,X3)
| ~ ren1(X3) )
& r1(X1,skf2(X1))
& ~ p3(skf2(X1))
& r1(X1,skf3(X1))
& ( p1(skf3(X1))
| p2(skf3(X1)) )
& ( ~ p2(skf3(X1))
| ~ p1(skf3(X1)) ) )
| ren2(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[skf1,skf2,skf3]),skolemize(X2,skf1(X1)),skolemize(X4,skf2(X1)),skolemize(X5,skf3(X1))],[ren2_elimImpEquivPushNegMiniScope]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_6,plain,
( ~ r1(X0,X1)
| ~ ren1(X1)
| ren2(X0) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[ren2_skol])]) ).
% FOF INTRODUCE RENAMING
fof(ren1_defn,definition,
! [X7] :
( ren1(X7)
<= ( ( p2(X7)
& ~ p1(X7) )
| ( ~ p2(X7)
& p1(X7) ) ) ),
introduced(definition,[new_symbols(definition,[ren1])],[main_nc_elimTB]) ).
% FOF SIMPLE INFERENCE
fof(ren1_elimImpEquivPushNegMiniScope,plain,
! [X1] :
( ( ( ~ p2(X1)
| p1(X1) )
& ( p2(X1)
| ~ p1(X1) ) )
| ren1(X1) ),
inference(elimImpEquivPushNegMiniScope,[status(thm)],[ren1_defn]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_3,plain,
( ~ p2(X0)
| p1(X0)
| ren1(X0) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[ren1_elimImpEquivPushNegMiniScope])]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_9,plain,
( r1(X0,skf3(X0))
| ren2(X0) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[ren2_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 RENAMING INFERENCE
fof(main_nc_renObv,negated_conjecture,
? [X1] :
~ ( ! [X2] :
( ~ r1(X1,X2)
| ~ p3(X2)
| ! [X3] :
( ~ r1(X2,X3)
| ~ p1(X3) ) )
| ! [X4] :
( ~ r1(X1,X4)
| ~ ! [X5] :
( ~ r1(X4,X5)
| ~ ren2(X5) ) ) ),
inference(renaming,[status(esa)],[main_nc_elimTB,ren1_defn,ren2_defn]) ).
% FOF SIMPLE INFERENCE
fof(main_nc_elimImpEquivPushNegMiniScope,negated_conjecture,
? [X1] :
( ? [X2] :
( r1(X1,X2)
& p3(X2)
& ? [X3] :
( r1(X2,X3)
& p1(X3) ) )
& ? [X4] :
( r1(X1,X4)
& ! [X5] :
( ~ r1(X4,X5)
| ~ ren2(X5) ) ) ),
inference(elimImpEquivPushNegMiniScope,[status(thm)],[main_nc_renObv]) ).
% FOF SKOLEM INFERENCE. WIP!!
fof(main_nc_skol,negated_conjecture,
( r1(skc4,skc5)
& p3(skc5)
& r1(skc5,skc6)
& p1(skc6)
& r1(skc4,skc7)
& ! [X5] :
( ~ r1(skc7,X5)
| ~ ren2(X5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[skc4,skc5,skc6,skc7]),skolemize(X1,skc4),skolemize(X2,skc5),skolemize(X3,skc6),skolemize(X4,skc7)],[main_nc_elimImpEquivPushNegMiniScope]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_17,plain,
( ~ r1(skc7,X0)
| ~ ren2(X0) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[main_nc_skol])]) ).
% CNF SPASS RESOLUTION.
cnf(c_19,plain,
~ ren2(skc7),
inference(resolution,[status(thm)],[c_1,c_17]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_4,plain,
( ~ p1(X0)
| p2(X0)
| ren1(X0) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[ren1_elimImpEquivPushNegMiniScope])]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_10,plain,
( p1(skf3(X0))
| p2(skf3(X0))
| ren2(X0) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[ren2_skol])]) ).
% CNF SPASS RESOLUTION.
cnf(c_20,plain,
( p1(skf3(skc7))
| p2(skf3(skc7)) ),
inference(resolution,[status(thm)],[c_10,c_19]) ).
% CNF SPASS RESOLUTION.
cnf(c_22,plain,
p2(skf3(skc7)),
inference(resolution,[status(thm)],[c_6,c_4,c_9,c_19,c_20]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_11,plain,
( ~ p2(skf3(X0))
| ~ p1(skf3(X0))
| ren2(X0) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[ren2_skol])]) ).
% CNF SPASS RESOLUTION.
cnf(c_23,plain,
( ~ p2(skf3(skc7))
| ~ p1(skf3(skc7)) ),
inference(resolution,[status(thm)],[c_11,c_19]) ).
% CNF SPASS RESOLUTION.
cnf(c_24,plain,
~ p1(skf3(skc7)),
inference(resolution,[status(thm)],[c_22,c_23]) ).
% CNF SPASS RESOLUTION.
cnf(c_25,plain,
$false,
inference(resolution,[status(thm)],[c_6,c_3,c_9,c_19,c_24,c_22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL686+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/SPASS-SCL-FOL -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n006.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 5 09:51:01 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running /export/starexec/sandbox/solver/bin/SPASS-SCL-FOL -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.37
% 0.13/0.37 % Input Clauses:
% 0.13/0.37 % 1:1:1:INP:Top: -> r1(x0,x0)
% 0.13/0.37 % 2:3:3:INP:TopTopTop: r1(x0,x1),r1(x1,x2) -> r1(x0,x2)
% 0.13/0.37 % 3:3:1:INP:Top: p2(x0) -> p1(x0),ren1(x0)
% 0.13/0.37 % 4:3:1:INP:Top: p1(x0) -> p2(x0),ren1(x0)
% 0.13/0.37 % 5:2:1:INP:Top: -> r1(x0,skf1(x0)),ren2(x0)
% 0.13/0.37 % 6:3:2:INP:TopTop: r1(x0,x1),ren1(x1) -> ren2(x0)
% 0.13/0.37 % 7:2:1:INP:Top: -> r1(x0,skf2(x0)),ren2(x0)
% 0.13/0.37 % 8:2:1:INP:Top: p3(skf2(x0)) -> ren2(x0)
% 0.13/0.37 % 9:2:1:INP:Top: -> r1(x0,skf3(x0)),ren2(x0)
% 0.13/0.37 % 10:3:1:INP:Top: -> p1(skf3(x0)),p2(skf3(x0)),ren2(x0)
% 0.13/0.37 % 11:3:1:INP:Top: p2(skf3(x0)),p1(skf3(x0)) -> ren2(x0)
% 0.13/0.37 % 12:1:0:INP:: -> r1(skc4,skc5)
% 0.13/0.37 % 13:1:0:INP:: -> p3(skc5)
% 0.13/0.37 % 14:1:0:INP:: -> r1(skc5,skc6)
% 0.13/0.37 % 15:1:0:INP:: -> p1(skc6)
% 0.13/0.37 % 16:1:0:INP:: -> r1(skc4,skc7)
% 0.13/0.37 % 17:2:1:INP:Top: r1(skc7,x0),ren2(x0) ->
% 0.13/0.37
% 0.13/0.37 % Predicates: r1 p3 p1 p2 ren1 ren2
% 0.13/0.37 % Fol Constants: skc4 skc5 skc6 skc7
% 0.13/0.37 % Fol Functions: skf1 skf2 skf3
% 0.13/0.37 % Problem Properties:
% 0.13/0.37 % This is a full first-order problem without equality. The Problem is non-linear.
% 0.13/0.37
% 0.13/0.37
% 0.13/0.37 % Reduced Input Axiom Clauses:
% 0.13/0.37 % 1:1:1:INP:Top: -> r1(x0,x0)
% 0.13/0.37 % 2:3:3:INP:TopTopTop: r1(x0,x1),r1(x1,x2) -> r1(x0,x2)
% 0.13/0.37 % 3:3:1:INP:Top: p2(x0) -> p1(x0),ren1(x0)
% 0.13/0.37 % 4:3:1:INP:Top: p1(x0) -> p2(x0),ren1(x0)
% 0.13/0.37 % 5:2:1:INP:Top: -> r1(x0,skf1(x0)),ren2(x0)
% 0.13/0.37 % 6:3:2:INP:TopTop: r1(x0,x1),ren1(x1) -> ren2(x0)
% 0.13/0.37 % 7:2:1:INP:Top: -> r1(x0,skf2(x0)),ren2(x0)
% 0.13/0.37 % 8:2:1:INP:Top: p3(skf2(x0)) -> ren2(x0)
% 0.13/0.37 % 9:2:1:INP:Top: -> r1(x0,skf3(x0)),ren2(x0)
% 0.13/0.37 % 10:3:1:INP:Top: -> p1(skf3(x0)),p2(skf3(x0)),ren2(x0)
% 0.13/0.37 % 11:3:1:INP:Top: p2(skf3(x0)),p1(skf3(x0)) -> ren2(x0)
% 0.13/0.37
% 0.13/0.37 % Reduced Input Conjecture Clauses:
% 0.13/0.37 % 12:1:0:INP:: -> r1(skc4,skc5)
% 0.13/0.37 % 13:1:0:INP:: -> p3(skc5)
% 0.13/0.37 % 14:1:0:INP:: -> r1(skc5,skc6)
% 0.13/0.37 % 15:1:0:INP:: -> p1(skc6)
% 0.13/0.37 % 16:1:0:INP:: -> r1(skc4,skc7)
% 0.13/0.37 % 17:2:1:INP:Top: r1(skc7,x0),ren2(x0) ->
% 0.13/0.37
% 0.13/0.37
% 0.13/0.37 % === Starting SPASS-SCL-FOL A Little Less Naive, considering 34 atoms initially. Used heuristic: lmodel_grow ===
% 0.13/0.37
% 0.13/0.37
% 0.13/0.37
% 0.13/0.37 % SZS status Theorem
% 0.13/0.37 % Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.37
% 0.13/0.37 % SPASS-SCL-FOL Statistics:
% 0.13/0.37 % Number of learned clauses: 6
% 0.13/0.37 % Number of propagations: 119
% 0.13/0.37 % Number of decisions: 56
% 0.13/0.37 % Number of resolutions: 14
% 0.13/0.37 % Number of condensations: 0
% 0.13/0.37 % Number of sub resolutions: 1
% 0.13/0.37
% 0.13/0.37 % Solver is done. Empty clause found
% 0.13/0.37
% 0.13/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.37
% 0.13/0.37
% 0.13/0.37 % Needed: 0:00:00.01
% 0.13/0.37
% 0.13/0.37 % ###
% 0.13/0.37 % ### Pagesize: 8192
% 0.13/0.37 % ### Marksize: 0
% 0.13/0.37 % ### Memory demanded: 870 KBytes
% 0.13/0.37 % ### Memory freed: 870 KBytes
% 0.13/0.37 % ### Memory remaining: 0 Bytes
% 0.13/0.37 % ### Pages allocated: 200 Pages
% 0.13/0.37 % ###
%------------------------------------------------------------------------------