%------------------------------------------------------------------------------
% File : SPASS-SCL---0.1.1
% Problem : LCL414+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : /export/starexec/sandbox/solver/bin/SPASS-SCL-FOL -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 01:09:30 PM UTC 2026
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 4 unt; 0 def)
% Number of atoms : 44 ( 0 equ)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 53 ( 20 ~; 13 |; 20 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 59 ( 1 sgn 45 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
% FILE RECORD
fof(thm147,conjecture,
~ ( ! [X1,X2] :
( ~ a_truth(implies(X1,X2))
| ~ a_truth(X1)
| a_truth(X2) )
& ! [X1,X2] : a_truth(implies(X1,implies(X2,X1)))
& ! [X1,X2,X3] : a_truth(implies(implies(X1,implies(X2,X3)),implies(implies(X1,X2),implies(X1,X3))))
& ! [X1,X2] : a_truth(implies(implies(not(X1),not(X2)),implies(X2,X1)))
& ? [X4] : ~ a_truth(implies(X4,X4)) ),
file('theBenchmark.p',thm147) ).
% NEGATING CONJECTURE
fof(thm147_nc,negated_conjecture,
( ! [X1,X2] :
( ~ a_truth(implies(X1,X2))
| ~ a_truth(X1)
| a_truth(X2) )
& ! [X1,X2] : a_truth(implies(X1,implies(X2,X1)))
& ! [X1,X2,X3] : a_truth(implies(implies(X1,implies(X2,X3)),implies(implies(X1,X2),implies(X1,X3))))
& ! [X1,X2] : a_truth(implies(implies(not(X1),not(X2)),implies(X2,X1)))
& ? [X4] : ~ a_truth(implies(X4,X4)) ),
inference(negating_conjecture,[status(cth)],[thm147]) ).
% FOF SIMPLE INFERENCE
fof(thm147_nc_elimTB,negated_conjecture,
( ! [X1,X2] :
( ~ a_truth(implies(X1,X2))
| ~ a_truth(X1)
| a_truth(X2) )
& ! [X3,X4] : a_truth(implies(X3,implies(X4,X3)))
& ! [X5,X6,X7] : a_truth(implies(implies(X5,implies(X6,X7)),implies(implies(X5,X6),implies(X5,X7))))
& ! [X8,X9] : a_truth(implies(implies(not(X8),not(X9)),implies(X9,X8)))
& ? [X10] : ~ a_truth(implies(X10,X10)) ),
inference(elimTB,[status(thm)],[inference(variable_rename,[status(thm)],[thm147_nc])]) ).
% FOF SIMPLE INFERENCE
fof(thm147_nc_elimImpEquivPushNegMiniScope,negated_conjecture,
( ! [X1,X2] :
( ~ a_truth(implies(X1,X2))
| ~ a_truth(X1)
| a_truth(X2) )
& ! [X3,X4] : a_truth(implies(X3,implies(X4,X3)))
& ! [X5,X6,X7] : a_truth(implies(implies(X5,implies(X6,X7)),implies(implies(X5,X6),implies(X5,X7))))
& ! [X8,X9] : a_truth(implies(implies(not(X8),not(X9)),implies(X9,X8)))
& ? [X10] : ~ a_truth(implies(X10,X10)) ),
inference(elimImpEquivPushNegMiniScope,[status(thm)],[thm147_nc_elimTB]) ).
% FOF SKOLEM INFERENCE. WIP!!
fof(thm147_nc_skol,negated_conjecture,
( ! [X1,X2] :
( ~ a_truth(implies(X1,X2))
| ~ a_truth(X1)
| a_truth(X2) )
& ! [X3,X4] : a_truth(implies(X3,implies(X4,X3)))
& ! [X5,X6,X7] : a_truth(implies(implies(X5,implies(X6,X7)),implies(implies(X5,X6),implies(X5,X7))))
& ! [X8,X9] : a_truth(implies(implies(not(X8),not(X9)),implies(X9,X8)))
& ~ a_truth(implies(skc1,skc1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[skc1]),skolemize(X10,skc1)],[thm147_nc_elimImpEquivPushNegMiniScope]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_1,plain,
( ~ a_truth(implies(X0,X1))
| ~ a_truth(X0)
| a_truth(X1) ),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[thm147_nc_skol])]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_3,plain,
a_truth(implies(implies(X0,implies(X1,X2)),implies(implies(X0,X1),implies(X0,X2)))),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[thm147_nc_skol])]) ).
% CNF SPASS RESOLUTION.
cnf(c_6,plain,
( ~ a_truth(implies(X0,implies(X1,X2)))
| a_truth(implies(implies(X0,X1),implies(X0,X2))) ),
inference(resolution,[status(thm)],[c_1,c_3]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_5,plain,
~ a_truth(implies(skc1,skc1)),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[thm147_nc_skol])]) ).
% FOF PUSH DISJ SPLITTING.
cnf(c_2,plain,
a_truth(implies(X0,implies(X1,X0))),
inference(split_conjunct,[status(thm)],[inference(push_disj,[status(thm)],[thm147_nc_skol])]) ).
% CNF SPASS RESOLUTION.
cnf(c_7,plain,
$false,
inference(resolution,[status(thm)],[c_1,c_6,c_5,c_2,c_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL414+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/SPASS-SCL-FOL -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n008.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 5 13:01:08 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running /export/starexec/sandbox/solver/bin/SPASS-SCL-FOL -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.39
% 0.12/0.39 % Input Clauses:
% 0.12/0.39 % 1:3:2:INP:TopTop: a_truth(implies(x0,x1)),a_truth(x0) -> a_truth(x1)
% 0.12/0.39 % 2:1:2:INP:TopTop: -> a_truth(implies(x0,implies(x1,x0)))
% 0.12/0.39 % 3:1:3:INP:TopTopTop: -> a_truth(implies(implies(x0,implies(x1,x2)),implies(implies(x0,x1),implies(x0,x2))))
% 0.12/0.39 % 4:1:2:INP:TopTop: -> a_truth(implies(implies(not(x0),not(x1)),implies(x1,x0)))
% 0.12/0.39 % 5:1:0:INP:: a_truth(implies(skc1,skc1)) ->
% 0.12/0.39
% 0.12/0.39 % Predicates: a_truth
% 0.12/0.39 % Fol Constants: skc1
% 0.12/0.39 % Fol Functions: implies not
% 0.12/0.39 % Problem Properties:
% 0.12/0.39 % This is a full first-order problem without equality. The Problem is non-linear.
% 0.12/0.39
% 0.12/0.39
% 0.12/0.39 % Reduced Input Axiom Clauses:
% 0.12/0.39
% 0.12/0.39 % Reduced Input Conjecture Clauses:
% 0.12/0.39 % 1:3:2:INP:TopTop: a_truth(implies(x0,x1)),a_truth(x0) -> a_truth(x1)
% 0.12/0.39 % 2:1:2:INP:TopTop: -> a_truth(implies(x0,implies(x1,x0)))
% 0.12/0.39 % 3:1:3:INP:TopTopTop: -> a_truth(implies(implies(x0,implies(x1,x2)),implies(implies(x0,x1),implies(x0,x2))))
% 0.12/0.39 % 4:1:2:INP:TopTop: -> a_truth(implies(implies(not(x0),not(x1)),implies(x1,x0)))
% 0.12/0.39 % 5:1:0:INP:: a_truth(implies(skc1,skc1)) ->
% 0.12/0.39
% 0.12/0.39
% 0.12/0.39 % === Starting SPASS-SCL-FOL A Little Less Naive, considering 75 atoms initially. Used heuristic: lcl ===
% 0.12/0.39
% 0.12/0.39
% 0.12/0.39
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.39
% 0.12/0.39 % SPASS-SCL-FOL Statistics:
% 0.12/0.39 % Number of learned clauses: 1
% 0.12/0.39 % Number of propagations: 22
% 0.12/0.39 % Number of decisions: 67
% 0.12/0.39 % Number of resolutions: 5
% 0.12/0.39 % Number of condensations: 0
% 0.12/0.39 % Number of sub resolutions: 0
% 0.12/0.39
% 0.12/0.39 % Solver is done. Empty clause found
% 0.12/0.39
% 0.12/0.39 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.39 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.39
% 0.12/0.39
% 0.12/0.39 % Needed: 0:00:00.02
% 0.12/0.39
% 0.12/0.39 % ###
% 0.12/0.39 % ### Pagesize: 8192
% 0.12/0.39 % ### Marksize: 0
% 0.12/0.39 % ### Memory demanded: 2581 KBytes
% 0.12/0.39 % ### Memory freed: 2581 KBytes
% 0.12/0.39 % ### Memory remaining: 0 Bytes
% 0.12/0.39 % ### Pages allocated: 365 Pages
% 0.12/0.39 % ###
%------------------------------------------------------------------------------