%------------------------------------------------------------------------------
% File : SPASS-SCL---0.1.1
% Problem : LCL439-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : /export/starexec/sandbox/solver/bin/SPASS-SCL-FOL -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 01:09:34 PM UTC 2026
% Result : Unsatisfiable 10.80s 11.11s
% Output : Proof 10.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 7
% Syntax : Number of clauses : 10 ( 5 unt; 0 nHn; 5 RR)
% Number of literals : 17 ( 0 equ; 8 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 26 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
% FILE RECORD
cnf(cls_Set_OinsertCI_1,axiom,
c_in(X0,c_insert(X0,X1,X2),X2),
file('theBenchmark.p',cls_Set_OinsertCI_1) ).
% FILE RECORD
cnf(cls_PropLog_Othms_OH_0,axiom,
( ~ c_in(X0,X1,tc_PropLog_Opl(X2))
| c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)) ),
file('theBenchmark.p',cls_PropLog_Othms_OH_0) ).
% CNF SPASS RESOLUTION.
cnf(c_10,plain,
c_in(X0,c_PropLog_Othms(c_insert(X0,X1,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),
inference(resolution,[status(thm)],[cls_Set_OinsertCI_1,cls_PropLog_Othms_OH_0]) ).
% FILE RECORD
cnf(cls_PropLog_Oweaken__left__insert_0,axiom,
( ~ c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2))
| c_in(X0,c_PropLog_Othms(c_insert(X3,X1,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)) ),
file('theBenchmark.p',cls_PropLog_Oweaken__left__insert_0) ).
% FILE RECORD
cnf(cls_PropLog_Othms__notE_0,axiom,
( ~ c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(X0,c_PropLog_Opl_Ofalse,X2),c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2))
| c_in(X3,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)) ),
file('theBenchmark.p',cls_PropLog_Othms__notE_0) ).
% FILE RECORD
cnf(cls_PropLog_Odeduction_0,axiom,
( ~ c_in(X0,c_PropLog_Othms(c_insert(X1,X2,tc_PropLog_Opl(X3)),X3),tc_PropLog_Opl(X3))
| c_in(c_PropLog_Opl_Oop_A_N_62(X1,X0,X3),c_PropLog_Othms(X2,X3),tc_PropLog_Opl(X3)) ),
file('theBenchmark.p',cls_PropLog_Odeduction_0) ).
% CNF SPASS RESOLUTION.
cnf(c_21,plain,
( ~ c_in(c_PropLog_Opl_Oop_A_N_62(X0,c_PropLog_Opl_Ofalse,X1),c_PropLog_Othms(X2,X1),tc_PropLog_Opl(X1))
| ~ c_in(X0,c_PropLog_Othms(c_insert(X3,X2,tc_PropLog_Opl(X1)),X1),tc_PropLog_Opl(X1))
| c_in(c_PropLog_Opl_Oop_A_N_62(X3,X4,X1),c_PropLog_Othms(X2,X1),tc_PropLog_Opl(X1)) ),
inference(resolution,[status(thm)],[cls_PropLog_Oweaken__left__insert_0,cls_PropLog_Othms__notE_0,cls_PropLog_Odeduction_0]) ).
% FILE RECORD
cnf(cls_conjecture_1,negated_conjecture,
~ c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
file('theBenchmark.p',cls_conjecture_1) ).
% FILE RECORD
cnf(cls_conjecture_0,negated_conjecture,
c_in(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)),
file('theBenchmark.p',cls_conjecture_0) ).
% CNF SPASS RESOLUTION.
cnf(c_25,plain,
$false,
inference(resolution,[status(thm)],[c_10,c_21,cls_conjecture_1,cls_conjecture_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL439-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/SPASS-SCL-FOL -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 6 01:32:09 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running /export/starexec/sandbox/solver/bin/SPASS-SCL-FOL -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.80/11.11
% 10.80/11.11 % Input Clauses:
% 10.80/11.11 % 1:2:4:INP:TopTopTopTop: c_in(x0,c_PropLog_Othms(c_insert(x1,x2,tc_PropLog_Opl(x3)),x3),tc_PropLog_Opl(x3)) -> c_in(c_PropLog_Opl_Oop_A_N_62(x1,x0,x3),c_PropLog_Othms(x2,x3),tc_PropLog_Opl(x3))
% 10.80/11.11 % 2:2:3:INP:TopTopTop: c_in(x0,x1,tc_PropLog_Opl(x2)) -> c_in(x0,c_PropLog_Othms(x1,x2),tc_PropLog_Opl(x2))
% 10.80/11.11 % 3:3:4:INP:TopTopTopTop: c_in(x0,c_PropLog_Othms(x1,x2),tc_PropLog_Opl(x2)),c_in(c_PropLog_Opl_Oop_A_N_62(x0,c_PropLog_Opl_Ofalse,x2),c_PropLog_Othms(x1,x2),tc_PropLog_Opl(x2)) -> c_in(x3,c_PropLog_Othms(x1,x2),tc_PropLog_Opl(x2))
% 10.80/11.11 % 4:2:4:INP:TopTopTopTop: c_in(x0,c_PropLog_Othms(x1,x2),tc_PropLog_Opl(x2)) -> c_in(x0,c_PropLog_Othms(c_insert(x3,x1,tc_PropLog_Opl(x2)),x2),tc_PropLog_Opl(x2))
% 10.80/11.11 % 5:1:3:INP:TopTopTop: -> c_in(x0,c_insert(x0,x1,x2),x2)
% 10.80/11.11 % 6:1:0:INP:: -> c_in(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a))
% 10.80/11.11 % 7:1:0:INP:: c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ->
% 10.80/11.11
% 10.80/11.11 % Predicates: c_in
% 10.80/11.11 % Fol Constants: c_PropLog_Opl_Ofalse v_p t_a v_H v_q
% 10.80/11.11 % Fol Functions: tc_PropLog_Opl c_insert c_PropLog_Othms c_PropLog_Opl_Oop_A_N_62
% 10.80/11.11 % Problem Properties:
% 10.80/11.11 % This is a full first-order problem without equality. The Problem is non-linear.
% 10.80/11.11
% 10.80/11.11
% 10.80/11.11 % Reduced Input Axiom Clauses:
% 10.80/11.11 % 1:2:4:INP:TopTopTopTop: c_in(x0,c_PropLog_Othms(c_insert(x1,x2,tc_PropLog_Opl(x3)),x3),tc_PropLog_Opl(x3)) -> c_in(c_PropLog_Opl_Oop_A_N_62(x1,x0,x3),c_PropLog_Othms(x2,x3),tc_PropLog_Opl(x3))
% 10.80/11.11 % 2:2:3:INP:TopTopTop: c_in(x0,x1,tc_PropLog_Opl(x2)) -> c_in(x0,c_PropLog_Othms(x1,x2),tc_PropLog_Opl(x2))
% 10.80/11.11 % 3:3:4:INP:TopTopTopTop: c_in(x0,c_PropLog_Othms(x1,x2),tc_PropLog_Opl(x2)),c_in(c_PropLog_Opl_Oop_A_N_62(x0,c_PropLog_Opl_Ofalse,x2),c_PropLog_Othms(x1,x2),tc_PropLog_Opl(x2)) -> c_in(x3,c_PropLog_Othms(x1,x2),tc_PropLog_Opl(x2))
% 10.80/11.11 % 4:2:4:INP:TopTopTopTop: c_in(x0,c_PropLog_Othms(x1,x2),tc_PropLog_Opl(x2)) -> c_in(x0,c_PropLog_Othms(c_insert(x3,x1,tc_PropLog_Opl(x2)),x2),tc_PropLog_Opl(x2))
% 10.80/11.11 % 5:1:3:INP:TopTopTop: -> c_in(x0,c_insert(x0,x1,x2),x2)
% 10.80/11.11
% 10.80/11.11 % Reduced Input Conjecture Clauses:
% 10.80/11.11 % 6:1:0:INP:: -> c_in(c_PropLog_Opl_Oop_A_N_62(v_p,c_PropLog_Opl_Ofalse,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a))
% 10.80/11.11 % 7:1:0:INP:: c_in(c_PropLog_Opl_Oop_A_N_62(v_p,v_q,t_a),c_PropLog_Othms(v_H,t_a),tc_PropLog_Opl(t_a)) ->
% 10.80/11.11
% 10.80/11.11
% 10.80/11.11 % === Starting SPASS-SCL-FOL A Little Less Naive, considering 14 atoms initially. Used heuristic: lmodel_grow ===
% 10.80/11.11
% 10.80/11.11
% 10.80/11.11
% 10.80/11.11 % SZS status Unsatisfiable
% 10.80/11.11 % Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.80/11.11
% 10.80/11.11 % SPASS-SCL-FOL Statistics:
% 10.80/11.11 % Number of learned clauses: 17
% 10.80/11.11 % Number of propagations: 10042
% 10.80/11.11 % Number of decisions: 5398
% 10.80/11.11 % Number of resolutions: 26
% 10.80/11.11 % Number of condensations: 1
% 10.80/11.11 % Number of sub resolutions: 0
% 10.80/11.11
% 10.80/11.11 % Solver is done. Empty clause found
% 10.80/11.11
% 10.80/11.11 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 10.80/11.11 % SZS output start Proof for theBenchmark
% See solution above
% 10.80/11.12 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 10.80/11.12
% 10.80/11.12
% 10.80/11.12 % Needed: 0:0:10.75
% 10.80/11.12
% 10.80/11.12 % ###
% 10.80/11.12 % ### Pagesize: 8192
% 10.80/11.12 % ### Marksize: 0
% 10.80/11.12 % ### Memory demanded: 40765 KBytes
% 10.80/11.12 % ### Memory freed: 40765 KBytes
% 10.80/11.12 % ### Memory remaining: 0 Bytes
% 10.80/11.12 % ### Pages allocated: 4072 Pages
% 10.80/11.12 % ###
%------------------------------------------------------------------------------