%------------------------------------------------------------------------------
% File : SPASS-SCL---0.1.1
% Problem : LCL656+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 : 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 01:09:59 PM UTC 2026
% Result : Theorem 0.09s 0.37s
% Output : Proof 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 7 unt; 4 def)
% Number of atoms : 217 ( 0 equ)
% Maximal formula atoms : 37 ( 8 avg)
% Number of connectives : 353 ( 161 ~; 108 |; 80 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 59 ( 0 sgn 46 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
% FILE RECORD
fof(main,conjecture,
~ ? [X1] :
~ ( ~ ! [X2] :
( ~ r1(X1,X2)
| p2(X2) )
| ~ ( ! [X2] :
( ~ r1(X1,X2)
| ( ( ( ~ ! [X1] :
( ~ r1(X2,X1)
| ~ ( ~ p2(X1)
& ~ p102(X1)
& p101(X1) ) )
& ~ ! [X1] :
( ~ r1(X2,X1)
| ~ ( p2(X1)
& ~ p102(X1)
& p101(X1) ) ) )
| ~ ( ~ p101(X2)
& p100(X2) ) )
& ( ( ( ! [X1] :
( ~ r1(X2,X1)
| ~ p2(X1)
| ~ p101(X1) )
| p2(X2) )
& ( ! [X1] :
( ~ r1(X2,X1)
| p2(X1)
| ~ p101(X1) )
| ~ p2(X2) ) )
| ~ p101(X2) )
& ( ( ( ! [X1] :
( ~ r1(X2,X1)
| ~ p1(X1)
| ~ p100(X1) )
| p1(X2) )
& ( ! [X1] :
( ~ r1(X2,X1)
| p1(X1)
| ~ p100(X1) )
| ~ p1(X2) ) )
| ~ p100(X2) )
& ( p101(X2)
| ~ p102(X2) )
& ( p100(X2)
| ~ p101(X2) ) ) )
& ~ p101(X1)
& p100(X1) ) ),
file('theBenchmark.p',main) ).
% NEGATING CONJECTURE
fof(main_nc,negated_conjecture,
? [X1] :
~ ( ~ ! [X2] :
( ~ r1(X1,X2)
| p2(X2) )
| ~ ( ! [X2] :
( ~ r1(X1,X2)
| ( ( ( ~ ! [X1] :
( ~ r1(X2,X1)
| ~ ( ~ p2(X1)
& ~ p102(X1)
& p101(X1) ) )
& ~ ! [X1] :
( ~ r1(X2,X1)
| ~ ( p2(X1)
& ~ p102(X1)
& p101(X1) ) ) )
| ~ ( ~ p101(X2)
& p100(X2) ) )
& ( ( ( ! [X1] :
( ~ r1(X2,X1)
| ~ p2(X1)
| ~ p101(X1) )
| p2(X2) )
& ( ! [X1] :
( ~ r1(X2,X1)
| p2(X1)
| ~ p101(X1) )
| ~ p2(X2) ) )
| ~ p101(X2) )
& ( ( ( ! [X1] :
( ~ r1(X2,X1)
| ~ p1(X1)
| ~ p100(X1) )
| p1(X2) )
& ( ! [X1] :
( ~ r1(X2,X1)
| p1(X1)
| ~ p100(X1) )
| ~ p1(X2) ) )
| ~ p100(X2) )
& ( p101(X2)
| ~ p102(X2) )
& ( p100(X2)
| ~ p101(X2) ) ) )
& ~ p101(X1)
& p100(X1) ) ),
inference(negating_conjecture,[status(cth)],[main]) ).
% FOF SIMPLE INFERENCE
fof(main_nc_elimTB,negated_conjecture,
? [X1] :
~ ( ~ ! [X2] :
( ~ r1(X1,X2)
| p2(X2) )
| ~ ( ! [X3] :
( ~ r1(X1,X3)
| ( ( ( ~ ! [X4] :
( ~ r1(X3,X4)
| ~ ( ~ p2(X4)
& ~ p102(X4)
& p101(X4) ) )
& ~ ! [X5] :
( ~ r1(X3,X5)
| ~ ( p2(X5)
& ~ p102(X5)
& p101(X5) ) ) )
| ~ ( ~ p101(X3)
& p100(X3) ) )
& ( ( ( ! [X6] :
( ~ r1(X3,X6)
| ~ p2(X6)
| ~ p101(X6) )
| p2(X3) )
& ( ! [X7] :
( ~ r1(X3,X7)
| p2(X7)
| ~ p101(X7) )
| ~ p2(X3) ) )
| ~ p101(X3) )
& ( ( ( ! [X8] :
( ~ r1(X3,X8)
| ~ p1(X8)
| ~ p100(X8) )
| p1(X3) )
& ( ! [X9] :
( ~ r1(X3,X9)
| p1(X9)
| ~ p100(X9) )
| ~ p1(X3) ) )
| ~ p100(X3) )
& ( p101(X3)
| ~ p102(X3) )
& ( p100(X3)
| ~ p101(X3) ) ) )
& ~ p101(X1)
& p100(X1) ) ),
inference(elimTB,[status(thm)],[inference(variable_rename,[status(thm)],[main_nc])]) ).
% FOF INTRODUCE RENAMING
fof(ren1_defn,definition,
! [X3] :
( ren1(X3)
=> ( ~ ! [X4] :
( ~ r1(X3,X4)
| ~ ( ~ p2(X4)
& ~ p102(X4)
& p101(X4) ) )
& ~ ! [X5] :
( ~ r1(X3,X5)
| ~ ( p2(X5)
& ~ p102(X5)
& p101(X5) ) ) ) ),
introduced(definition,[new_symbols(definition,[ren1])],[main_nc_elimTB]) ).
% FOF INTRODUCE RENAMING
fof(ren2_defn,definition,
! [X3] :
( ren2(X3)
=> ( ( ! [X6] :
( ~ r1(X3,X6)
| ~ p2(X6)
| ~ p101(X6) )
| p2(X3) )
& ( ! [X7] :
( ~ r1(X3,X7)
| p2(X7)
| ~ p101(X7) )
| ~ p2(X3) ) ) ),
introduced(definition,[new_symbols(definition,[ren2])],[main_nc_elimTB]) ).
% FOF INTRODUCE RENAMING
fof(ren3_defn,definition,
! [X3] :
( ren3(X3)
=> ( ( ! [X8] :
( ~ r1(X3,X8)
| ~ p1(X8)
| ~ p100(X8) )
| p1(X3) )
& ( ! [X9] :
( ~ r1(X3,X9)
| p1(X9)
| ~ p100(X9) )
| ~ p1(X3) ) ) ),
introduced(definition,[new_symbols(definition,[ren3])],[main_nc_elimTB]) ).
% FOF INTRODUCE RENAMING
fof(ren4_defn,definition,
! [X3] :
( ren4(X3)
=> ( ( ren1(X3)
| ~ ( ~ p101(X3)
& p100(X3) ) )
& ( ren2(X3)
| ~ p101(X3) )
& ( ren3(X3)
| ~ p100(X3) )
& ( p101(X3)
| ~ p102(X3) )
& ( p100(X3)
| ~ p101(X3) ) ) ),
introduced(definition,[new_symbols(definition,[ren4])],[main_nc_elimTB]) ).
% FOF RENAMING INFERENCE
fof(main_nc_renObv,negated_conjecture,
? [X1] :
~ ( ~ ! [X2] :
( ~ r1(X1,X2)
| p2(X2) )
| ~ ( ! [X3] :
( ~ r1(X1,X3)
| ren4(X3) )
& ~ p101(X1)
& p100(X1) ) ),
inference(renaming,[status(esa)],[main_nc_elimTB,ren1_defn,ren2_defn,ren3_defn,ren4_defn]) ).
% FOF SIMPLE INFERENCE
fof(main_nc_elimImpEquivPushNegMiniScope,negated_conjecture,
? [X1] :
( ! [X2] :
( ~ r1(X1,X2)
| p2(X2) )
& ! [X3] :
( ~ r1(X1,X3)
| ren4(X3) )
& ~ p101(X1)
& p100(X1) ),
inference(elimImpEquivPushNegMiniScope,[status(thm)],[main_nc_renObv]) ).
% FOF SKOLEM INFERENCE. WIP!!
fof(main_nc_skol,negated_conjecture,
( ! [X2] :
( ~ r1(skc3,X2)
| p2(X2) )
& ! [X3] :
( ~ r1(skc3,X3)
| ren4(X3) )
& ~ p101(skc3)
& p100(skc3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[skc3]),skolemize(X1,skc3)],[main_nc_elimImpEquivPushNegMiniScope]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_19,plain,
( ~ r1(skc3,X0)
| p2(X0) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[main_nc_skol])]) ).
% FOF SIMPLE INFERENCE
fof(ren1_elimImpEquivPushNegMiniScope,plain,
! [X1] :
( ~ ren1(X1)
| ( ? [X2] :
( r1(X1,X2)
& ~ p2(X2)
& ~ p102(X2)
& p101(X2) )
& ? [X3] :
( r1(X1,X3)
& p2(X3)
& ~ p102(X3)
& p101(X3) ) ) ),
inference(elimImpEquivPushNegMiniScope,[status(thm)],[ren1_defn]) ).
% FOF SKOLEM INFERENCE. WIP!!
fof(ren1_skol,plain,
! [X1] :
( ~ ren1(X1)
| ( r1(X1,skf1(X1))
& ~ p2(skf1(X1))
& ~ p102(skf1(X1))
& p101(skf1(X1))
& r1(X1,skf2(X1))
& p2(skf2(X1))
& ~ p102(skf2(X1))
& p101(skf2(X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[skf1,skf2]),skolemize(X2,skf1(X1)),skolemize(X3,skf2(X1))],[ren1_elimImpEquivPushNegMiniScope]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_3,plain,
( ~ ren1(X0)
| ~ p2(skf1(X0)) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[ren1_skol])]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_2,plain,
( ~ ren1(X0)
| r1(X0,skf1(X0)) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[ren1_skol])]) ).
% FOF SIMPLE INFERENCE
fof(ren4_elimImpEquivPushNegMiniScope,plain,
! [X1] :
( ~ ren4(X1)
| ( ( ren1(X1)
| p101(X1)
| ~ p100(X1) )
& ( ren2(X1)
| ~ p101(X1) )
& ( ren3(X1)
| ~ p100(X1) )
& ( p101(X1)
| ~ p102(X1) )
& ( p100(X1)
| ~ p101(X1) ) ) ),
inference(elimImpEquivPushNegMiniScope,[status(thm)],[ren4_defn]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_14,plain,
( ~ ren4(X0)
| ~ p100(X0)
| ren1(X0)
| p101(X0) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[ren4_elimImpEquivPushNegMiniScope])]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_20,plain,
( ~ r1(skc3,X0)
| ren4(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_21,plain,
~ p101(skc3),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[main_nc_skol])]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_22,plain,
p100(skc3),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[main_nc_skol])]) ).
% CNF SPASS RESOLUTION.
cnf(c_27,plain,
$false,
inference(resolution,[status(thm)],[c_19,c_3,c_2,c_14,c_20,c_1,c_21,c_22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL656+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
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 5 02:18:40 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running /export/starexec/sandbox2/solver/bin/SPASS-SCL-FOL -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37
% 0.09/0.37 % Input Clauses:
% 0.09/0.37 % 1:1:1:INP:Top: -> r1(x0,x0)
% 0.09/0.37 % 2:2:1:INP:Top: ren1(x0) -> r1(x0,skf1(x0))
% 0.09/0.37 % 3:2:1:INP:Top: ren1(x0),p2(skf1(x0)) ->
% 0.09/0.37 % 4:2:1:INP:Top: ren1(x0),p102(skf1(x0)) ->
% 0.09/0.37 % 5:2:1:INP:Top: ren1(x0) -> p101(skf1(x0))
% 0.09/0.37 % 6:2:1:INP:Top: ren1(x0) -> r1(x0,skf2(x0))
% 0.09/0.37 % 7:2:1:INP:Top: ren1(x0) -> p2(skf2(x0))
% 0.09/0.37 % 8:2:1:INP:Top: ren1(x0),p102(skf2(x0)) ->
% 0.09/0.37 % 9:2:1:INP:Top: ren1(x0) -> p101(skf2(x0))
% 0.09/0.37 % 10:5:2:INP:TopTop: ren2(x0),r1(x0,x1),p2(x1),p101(x1) -> p2(x0)
% 0.09/0.37 % 11:5:2:INP:TopTop: ren2(x0),r1(x0,x1),p101(x1),p2(x0) -> p2(x1)
% 0.09/0.37 % 12:5:2:INP:TopTop: ren3(x0),r1(x0,x1),p1(x1),p100(x1) -> p1(x0)
% 0.09/0.37 % 13:5:2:INP:TopTop: ren3(x0),r1(x0,x1),p100(x1),p1(x0) -> p1(x1)
% 0.09/0.37 % 14:4:1:INP:Top: ren4(x0),p100(x0) -> ren1(x0),p101(x0)
% 0.09/0.37 % 15:3:1:INP:Top: ren4(x0),p101(x0) -> ren2(x0)
% 0.09/0.37 % 16:3:1:INP:Top: ren4(x0),p100(x0) -> ren3(x0)
% 0.09/0.37 % 17:3:1:INP:Top: ren4(x0),p102(x0) -> p101(x0)
% 0.09/0.37 % 18:3:1:INP:Top: ren4(x0),p101(x0) -> p100(x0)
% 0.09/0.37 % 19:2:1:INP:Top: r1(skc3,x0) -> p2(x0)
% 0.09/0.37 % 20:2:1:INP:Top: r1(skc3,x0) -> ren4(x0)
% 0.09/0.37 % 21:1:0:INP:: p101(skc3) ->
% 0.09/0.37 % 22:1:0:INP:: -> p100(skc3)
% 0.09/0.37
% 0.09/0.37 % Predicates: r1 p2 p102 p101 p100 p1 ren1 ren2 ren3 ren4
% 0.09/0.37 % Fol Constants: skc3
% 0.09/0.37 % Fol Functions: skf1 skf2
% 0.09/0.37 % Problem Properties:
% 0.09/0.37 % This is a full first-order problem without equality. The Problem is non-linear.
% 0.09/0.37
% 0.09/0.37
% 0.09/0.37 % Reduced Input Axiom Clauses:
% 0.09/0.37 % 1:1:1:INP:Top: -> r1(x0,x0)
% 0.09/0.37 % 2:2:1:INP:Top: ren1(x0) -> r1(x0,skf1(x0))
% 0.09/0.37 % 3:2:1:INP:Top: ren1(x0),p2(skf1(x0)) ->
% 0.09/0.37 % 4:2:1:INP:Top: ren1(x0),p102(skf1(x0)) ->
% 0.09/0.37 % 5:2:1:INP:Top: ren1(x0) -> p101(skf1(x0))
% 0.09/0.37 % 6:2:1:INP:Top: ren1(x0) -> r1(x0,skf2(x0))
% 0.09/0.37 % 7:2:1:INP:Top: ren1(x0) -> p2(skf2(x0))
% 0.09/0.37 % 8:2:1:INP:Top: ren1(x0),p102(skf2(x0)) ->
% 0.09/0.37 % 9:2:1:INP:Top: ren1(x0) -> p101(skf2(x0))
% 0.09/0.37 % 10:5:2:INP:TopTop: ren2(x0),r1(x0,x1),p2(x1),p101(x1) -> p2(x0)
% 0.09/0.37 % 11:5:2:INP:TopTop: ren2(x0),r1(x0,x1),p101(x1),p2(x0) -> p2(x1)
% 0.09/0.37 % 12:5:2:INP:TopTop: ren3(x0),r1(x0,x1),p1(x1),p100(x1) -> p1(x0)
% 0.09/0.37 % 13:5:2:INP:TopTop: ren3(x0),r1(x0,x1),p100(x1),p1(x0) -> p1(x1)
% 0.09/0.37 % 14:4:1:INP:Top: ren4(x0),p100(x0) -> ren1(x0),p101(x0)
% 0.09/0.37 % 15:3:1:INP:Top: ren4(x0),p101(x0) -> ren2(x0)
% 0.09/0.37 % 16:3:1:INP:Top: ren4(x0),p100(x0) -> ren3(x0)
% 0.09/0.37 % 17:3:1:INP:Top: ren4(x0),p102(x0) -> p101(x0)
% 0.09/0.37 % 18:3:1:INP:Top: ren4(x0),p101(x0) -> p100(x0)
% 0.09/0.37
% 0.09/0.37 % Reduced Input Conjecture Clauses:
% 0.09/0.37 % 19:2:1:INP:Top: r1(skc3,x0) -> p2(x0)
% 0.09/0.37 % 20:2:1:INP:Top: r1(skc3,x0) -> ren4(x0)
% 0.09/0.37 % 21:1:0:INP:: p101(skc3) ->
% 0.09/0.37 % 22:1:0:INP:: -> p100(skc3)
% 0.09/0.37
% 0.09/0.37
% 0.09/0.37 % === Starting SPASS-SCL-FOL A Little Less Naive, considering 27 atoms initially. Used heuristic: lmodel_grow ===
% 0.09/0.37
% 0.09/0.37
% 0.09/0.37
% 0.09/0.37 % SZS status Theorem
% 0.09/0.37 % Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37
% 0.09/0.37 % SPASS-SCL-FOL Statistics:
% 0.09/0.37 % Number of learned clauses: 4
% 0.09/0.37 % Number of propagations: 23
% 0.09/0.37 % Number of decisions: 18
% 0.09/0.37 % Number of resolutions: 11
% 0.09/0.37 % Number of condensations: 0
% 0.09/0.37 % Number of sub resolutions: 0
% 0.09/0.37
% 0.09/0.37 % Solver is done. Empty clause found
% 0.09/0.37
% 0.09/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.09/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.09/0.37
% 0.09/0.37
% 0.09/0.37 % Needed: 0:00:00.00
% 0.09/0.37
% 0.09/0.37 % ###
% 0.09/0.37 % ### Pagesize: 8192
% 0.09/0.37 % ### Marksize: 0
% 0.09/0.37 % ### Memory demanded: 388 KBytes
% 0.09/0.37 % ### Memory freed: 388 KBytes
% 0.09/0.37 % ### Memory remaining: 0 Bytes
% 0.09/0.37 % ### Pages allocated: 129 Pages
% 0.09/0.37 % ###
%------------------------------------------------------------------------------