%------------------------------------------------------------------------------
% File : SPASS-SCL---0.1.1
% Problem : LCL682+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 : n014.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 01:10:12 PM UTC 2026
% Result : Theorem 0.09s 0.37s
% Output : Proof 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 4 unt; 1 def)
% Number of atoms : 132 ( 0 equ)
% Maximal formula atoms : 21 ( 9 avg)
% Number of connectives : 219 ( 101 ~; 90 |; 27 &)
% ( 0 <=>; 0 =>; 1 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 9 con; 0-0 aty)
% Number of variables : 76 ( 0 sgn 60 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
% FILE RECORD
fof(main,conjecture,
~ ? [X1] :
~ ( ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ( ~ ! [X1] :
( ~ r1(X2,X1)
| p16(X1) )
| ~ ! [X1] :
( ~ r1(X2,X1)
| p12(X1) )
| ~ ! [X1] :
( ~ r1(X2,X1)
| p14(X1) )
| ~ ! [X1] :
( ~ r1(X2,X1)
| p12(X1) ) ) )
| ! [X2] :
( ~ r1(X1,X2)
| ! [X1] :
( ~ r1(X2,X1)
| p15(X1) ) )
| ! [X2] :
( ~ r1(X1,X2)
| ! [X1] :
( ~ r1(X2,X1)
| p13(X1) ) )
| ! [X2] :
( ~ r1(X1,X2)
| ! [X1] :
( ~ r1(X2,X1)
| p12(X1) ) )
| ! [X2] :
( ~ r1(X1,X2)
| ! [X1] :
( ~ r1(X2,X1)
| p11(X1) ) ) ),
file('theBenchmark.p',main) ).
% NEGATING CONJECTURE
fof(main_nc,negated_conjecture,
? [X1] :
~ ( ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ( ~ ! [X1] :
( ~ r1(X2,X1)
| p16(X1) )
| ~ ! [X1] :
( ~ r1(X2,X1)
| p12(X1) )
| ~ ! [X1] :
( ~ r1(X2,X1)
| p14(X1) )
| ~ ! [X1] :
( ~ r1(X2,X1)
| p12(X1) ) ) )
| ! [X2] :
( ~ r1(X1,X2)
| ! [X1] :
( ~ r1(X2,X1)
| p15(X1) ) )
| ! [X2] :
( ~ r1(X1,X2)
| ! [X1] :
( ~ r1(X2,X1)
| p13(X1) ) )
| ! [X2] :
( ~ r1(X1,X2)
| ! [X1] :
( ~ r1(X2,X1)
| p12(X1) ) )
| ! [X2] :
( ~ r1(X1,X2)
| ! [X1] :
( ~ r1(X2,X1)
| p11(X1) ) ) ),
inference(negating_conjecture,[status(cth)],[main]) ).
% FOF SIMPLE INFERENCE
fof(main_nc_elimTB,negated_conjecture,
? [X1] :
~ ( ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ( ~ ! [X3] :
( ~ r1(X2,X3)
| p16(X3) )
| ~ ! [X4] :
( ~ r1(X2,X4)
| p12(X4) )
| ~ ! [X5] :
( ~ r1(X2,X5)
| p14(X5) )
| ~ ! [X6] :
( ~ r1(X2,X6)
| p12(X6) ) ) )
| ! [X7] :
( ~ r1(X1,X7)
| ! [X8] :
( ~ r1(X7,X8)
| p15(X8) ) )
| ! [X9] :
( ~ r1(X1,X9)
| ! [X10] :
( ~ r1(X9,X10)
| p13(X10) ) )
| ! [X11] :
( ~ r1(X1,X11)
| ! [X12] :
( ~ r1(X11,X12)
| p12(X12) ) )
| ! [X13] :
( ~ r1(X1,X13)
| ! [X14] :
( ~ r1(X13,X14)
| p11(X14) ) ) ),
inference(elimTB,[status(thm)],[inference(variable_rename,[status(thm)],[main_nc])]) ).
% FOF INTRODUCE RENAMING
fof(ren1_defn,definition,
! [X2] :
( ren1(X2)
<= ( ~ ! [X3] :
( ~ r1(X2,X3)
| p16(X3) )
| ~ ! [X4] :
( ~ r1(X2,X4)
| p12(X4) )
| ~ ! [X5] :
( ~ r1(X2,X5)
| p14(X5) )
| ~ ! [X6] :
( ~ r1(X2,X6)
| p12(X6) ) ) ),
introduced(definition,[new_symbols(definition,[ren1])],[main_nc_elimTB]) ).
% FOF RENAMING INFERENCE
fof(main_nc_renObv,negated_conjecture,
? [X1] :
~ ( ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ren1(X2) )
| ! [X7] :
( ~ r1(X1,X7)
| ! [X8] :
( ~ r1(X7,X8)
| p15(X8) ) )
| ! [X9] :
( ~ r1(X1,X9)
| ! [X10] :
( ~ r1(X9,X10)
| p13(X10) ) )
| ! [X11] :
( ~ r1(X1,X11)
| ! [X12] :
( ~ r1(X11,X12)
| p12(X12) ) )
| ! [X13] :
( ~ r1(X1,X13)
| ! [X14] :
( ~ r1(X13,X14)
| p11(X14) ) ) ),
inference(renaming,[status(esa)],[main_nc_elimTB,ren1_defn]) ).
% FOF SIMPLE INFERENCE
fof(main_nc_elimImpEquivPushNegMiniScope,negated_conjecture,
? [X1] :
( ! [X2] :
( ~ r1(X1,X2)
| ~ ren1(X2) )
& ? [X3] :
( r1(X1,X3)
& ? [X4] :
( r1(X3,X4)
& ~ p15(X4) ) )
& ? [X5] :
( r1(X1,X5)
& ? [X6] :
( r1(X5,X6)
& ~ p13(X6) ) )
& ? [X7] :
( r1(X1,X7)
& ? [X8] :
( r1(X7,X8)
& ~ p12(X8) ) )
& ? [X9] :
( r1(X1,X9)
& ? [X10] :
( r1(X9,X10)
& ~ p11(X10) ) ) ),
inference(elimImpEquivPushNegMiniScope,[status(thm)],[main_nc_renObv]) ).
% FOF SKOLEM INFERENCE. WIP!!
fof(main_nc_skol,negated_conjecture,
( ! [X2] :
( ~ r1(skc1,X2)
| ~ ren1(X2) )
& r1(skc1,skc2)
& r1(skc2,skc3)
& ~ p15(skc3)
& r1(skc1,skc4)
& r1(skc4,skc5)
& ~ p13(skc5)
& r1(skc1,skc6)
& r1(skc6,skc7)
& ~ p12(skc7)
& r1(skc1,skc8)
& r1(skc8,skc9)
& ~ p11(skc9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[skc1,skc2,skc3,skc4,skc5,skc6,skc7,skc8,skc9]),skolemize(X1,skc1),skolemize(X3,skc2),skolemize(X4,skc3),skolemize(X5,skc4),skolemize(X6,skc5),skolemize(X7,skc6),skolemize(X8,skc7),skolemize(X9,skc8),skolemize(X10,skc9)],[main_nc_elimImpEquivPushNegMiniScope]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_7,plain,
( ~ r1(skc1,X0)
| ~ ren1(X0) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[main_nc_skol])]) ).
% FOF SIMPLE INFERENCE
fof(ren1_elimImpEquivPushNegMiniScope,plain,
! [X1] :
( ( ! [X2] :
( ~ r1(X1,X2)
| p16(X2) )
& ! [X3] :
( ~ r1(X1,X3)
| p12(X3) )
& ! [X4] :
( ~ r1(X1,X4)
| p14(X4) )
& ! [X5] :
( ~ r1(X1,X5)
| p12(X5) ) )
| ren1(X1) ),
inference(elimImpEquivPushNegMiniScope,[status(thm)],[ren1_defn]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_6,plain,
( ~ r1(X0,X1)
| p12(X1)
| ren1(X0) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[ren1_elimImpEquivPushNegMiniScope])]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_14,plain,
r1(skc1,skc6),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[main_nc_skol])]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_15,plain,
r1(skc6,skc7),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[main_nc_skol])]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_16,plain,
~ p12(skc7),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[main_nc_skol])]) ).
% CNF SPASS RESOLUTION.
cnf(c_20,plain,
$false,
inference(resolution,[status(thm)],[c_7,c_6,c_14,c_15,c_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL682+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
% 0.09/0.36 % Computer : n014.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 : Fri Sep 4 16:06:57 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running /export/starexec/sandbox/solver/bin/SPASS-SCL-FOL -t 300 /export/starexec/sandbox/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 % 2:3:3:INP:TopTopTop: r1(x0,x1),r1(x1,x2) -> r1(x0,x2)
% 0.09/0.37 % 3:3:2:INP:TopTop: r1(x0,x1) -> p16(x1),ren1(x0)
% 0.09/0.37 % 4:3:2:INP:TopTop: r1(x0,x1) -> p12(x1),ren1(x0)
% 0.09/0.37 % 5:3:2:INP:TopTop: r1(x0,x1) -> p14(x1),ren1(x0)
% 0.09/0.37 % 6:3:2:INP:TopTop: r1(x0,x1) -> p12(x1),ren1(x0)
% 0.09/0.37 % 7:2:1:INP:Top: r1(skc1,x0),ren1(x0) ->
% 0.09/0.37 % 8:1:0:INP:: -> r1(skc1,skc2)
% 0.09/0.37 % 9:1:0:INP:: -> r1(skc2,skc3)
% 0.09/0.37 % 10:1:0:INP:: p15(skc3) ->
% 0.09/0.37 % 11:1:0:INP:: -> r1(skc1,skc4)
% 0.09/0.37 % 12:1:0:INP:: -> r1(skc4,skc5)
% 0.09/0.37 % 13:1:0:INP:: p13(skc5) ->
% 0.09/0.37 % 14:1:0:INP:: -> r1(skc1,skc6)
% 0.09/0.37 % 15:1:0:INP:: -> r1(skc6,skc7)
% 0.09/0.37 % 16:1:0:INP:: p12(skc7) ->
% 0.09/0.37 % 17:1:0:INP:: -> r1(skc1,skc8)
% 0.09/0.37 % 18:1:0:INP:: -> r1(skc8,skc9)
% 0.09/0.37 % 19:1:0:INP:: p11(skc9) ->
% 0.09/0.37
% 0.09/0.37 % Predicates: r1 p16 p12 p14 p15 p13 p11 ren1
% 0.09/0.37 % Fol Constants: skc1 skc2 skc3 skc4 skc5 skc6 skc7 skc8 skc9
% 0.09/0.37 % Fol Functions:
% 0.09/0.37 % Problem Properties:
% 0.09/0.37 % This is a Bernays Schoenfinkel problem. 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 % 2:3:3:INP:TopTopTop: r1(x0,x1),r1(x1,x2) -> r1(x0,x2)
% 0.09/0.37 % 3:3:2:INP:TopTop: r1(x0,x1) -> p16(x1),ren1(x0)
% 0.09/0.37 % 5:3:2:INP:TopTop: r1(x0,x1) -> p14(x1),ren1(x0)
% 0.09/0.37 % 6:3:2:INP:TopTop: r1(x0,x1) -> p12(x1),ren1(x0)
% 0.09/0.37
% 0.09/0.37 % Reduced Input Conjecture Clauses:
% 0.09/0.37 % 19:1:0:INP:: p11(skc9) ->
% 0.09/0.37 % 7:2:1:INP:Top: r1(skc1,x0),ren1(x0) ->
% 0.09/0.37 % 8:1:0:INP:: -> r1(skc1,skc2)
% 0.09/0.37 % 9:1:0:INP:: -> r1(skc2,skc3)
% 0.09/0.37 % 10:1:0:INP:: p15(skc3) ->
% 0.09/0.37 % 11:1:0:INP:: -> r1(skc1,skc4)
% 0.09/0.37 % 12:1:0:INP:: -> r1(skc4,skc5)
% 0.09/0.37 % 13:1:0:INP:: p13(skc5) ->
% 0.09/0.37 % 14:1:0:INP:: -> r1(skc1,skc6)
% 0.09/0.37 % 15:1:0:INP:: -> r1(skc6,skc7)
% 0.09/0.37 % 16:1:0:INP:: p12(skc7) ->
% 0.09/0.37 % 17:1:0:INP:: -> r1(skc1,skc8)
% 0.09/0.37 % 18:1:0:INP:: -> r1(skc8,skc9)
% 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/sandbox/benchmark/theBenchmark.p
% 0.09/0.37
% 0.09/0.37 % SPASS-SCL-FOL Statistics:
% 0.09/0.37 % Number of learned clauses: 0
% 0.09/0.37 % Number of propagations: 10
% 0.09/0.37 % Number of decisions: 0
% 0.09/0.37 % Number of resolutions: 4
% 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: 334 KBytes
% 0.09/0.37 % ### Memory freed: 334 KBytes
% 0.09/0.37 % ### Memory remaining: 0 Bytes
% 0.09/0.37 % ### Pages allocated: 117 Pages
% 0.09/0.37 % ###
%------------------------------------------------------------------------------