%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL431-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n013.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 : Fri Sep 25 02:06:36 PM UTC 2026
% Result : Unsatisfiable 1.66s 1.31s
% Output : CNFRefutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 20 ( 17 unt; 3 def)
% Number of atoms : 37 ( 10 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 13 ( 8 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 23 ( 0 sgn 23 !; 0 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
c_PropLog_Osat(c_emptyset,v_p,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2,negated_conjecture,
~ c_in(v_p,c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3,axiom,
! [X2,X3,X0,X1] :
( c_in(X0,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(X0,X2,X1),c_PropLog_Ohyps(X0,X3,X1),tc_set(tc_PropLog_Opl(X1))),X1),tc_PropLog_Opl(X1))
| ~ c_PropLog_Osat(c_emptyset,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Ocompleteness__0__lemma__dest_0) ).
fof(f4,axiom,
! [X0,X1] : c_minus(X0,X0,tc_set(X1)) = c_emptyset,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__cancel_0) ).
fof(f5,plain,
! [X0,X1] : c_emptyset = c_minus(X0,X0,tc_set(X1)),
inference(reorient_equations,[],[f4]) ).
tcf(c_53,negated_conjecture,
c_PropLog_Osat(c_emptyset,v_p,t_a),
inference(cnf_transformation,[],[f1]) ).
tcf(c_54,negated_conjecture,
~ c_in(v_p,c_PropLog_Othms(c_emptyset,t_a),tc_PropLog_Opl(t_a)),
inference(cnf_transformation,[],[f2]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X0,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(X0,X2,X1),c_PropLog_Ohyps(X0,X3,X1),tc_set(tc_PropLog_Opl(X1))),X1),tc_PropLog_Opl(X1))
| ~ c_PropLog_Osat(c_emptyset,X0,X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] : c_minus(X0,X0,tc_set(X1)) = c_emptyset,
inference(cnf_transformation,[],[f5]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X0,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(X0,X2,X1),c_PropLog_Ohyps(X0,X3,X1),tc_set(tc_PropLog_Opl(X1))),X1),tc_PropLog_Opl(X1))
| ( c_emptyset != c_emptyset )
| ( X1 != t_a )
| ( X0 != v_p ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_55]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] : c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,X0,t_a),c_PropLog_Ohyps(v_p,X1,t_a),tc_set(tc_PropLog_Opl(t_a))),t_a),tc_PropLog_Opl(t_a)),
inference(unflattening,[status(thm)],[c_80]) ).
tcf(c_129,definition,
iPr_def_10 = tc_PropLog_Opl(t_a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_130,definition,
iPr_def_11 = tc_set(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_131,definition,
iPr_def_12 = c_PropLog_Othms(c_emptyset,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_132,plain,
! [X0: $i,X1: $i] : c_in(v_p,c_PropLog_Othms(c_minus(c_PropLog_Ohyps(v_p,X0,t_a),c_PropLog_Ohyps(v_p,X1,t_a),iPr_def_11),t_a),iPr_def_10),
inference(demodulation,[status(thm)],[c_81,c_129,c_130]) ).
tcf(c_133,negated_conjecture,
~ c_in(v_p,iPr_def_12,iPr_def_10),
inference(demodulation,[status(thm)],[c_54,c_131]) ).
tcf(c_269,plain,
! [X0: $i] : c_minus(X0,X0,iPr_def_11) = c_emptyset,
inference(superposition,[status(thm)],[c_130,c_56]) ).
tcf(c_271,plain,
c_in(v_p,c_PropLog_Othms(c_emptyset,t_a),iPr_def_10),
inference(superposition,[status(thm)],[c_269,c_132]) ).
tcf(c_272,plain,
c_in(v_p,iPr_def_12,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_271,c_131]) ).
tcf(c_273,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_272,c_133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL431-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 % Computer : n013.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Wed Sep 23 23:19:37 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.45
% 0.13/0.45 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.45
% 0.13/0.45 % Detected problem language: tptp
% 0.20/0.46 % Proving...
% 1.66/1.31 % SZS status Started for theBenchmark.p
% 1.66/1.31 % SZS status Unsatisfiable for theBenchmark.p
% 1.66/1.31
% 1.66/1.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.66/1.31
% 1.66/1.31 % ------ iProver source info
% 1.66/1.31
% 1.66/1.31 % git: date: 2026-07-19 20:42:38 +0200
% 1.66/1.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.66/1.31 % git: non_committed_changes: false
% 1.66/1.31
% 1.66/1.31 % ------ Parsing...% successful
% 1.66/1.31
% 1.66/1.31
% 1.66/1.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.66/1.31
% 1.66/1.31 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 1.66/1.31
% 1.66/1.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.66/1.31
% 1.66/1.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.66/1.31 % ------ Proving...
% 1.66/1.31 % ------ Problem Properties
% 1.66/1.31
% 1.66/1.31 %
% 1.66/1.31 % clauses 6
% 1.66/1.31 % conjectures 1
% 1.66/1.31 % EPR 1
% 1.66/1.31 % Horn 6
% 1.66/1.31 % unary 6
% 1.66/1.31 % binary 0
% 1.66/1.31 % lits 6
% 1.66/1.32 % lits eq 4
% 1.66/1.32 % fd_pure 0
% 1.66/1.32 % fd_pseudo 0
% 1.66/1.32 % fd_cond 0
% 1.66/1.32 % fd_pseudo_cond 0
% 1.66/1.32 % AC symbols 0
% 1.66/1.32
% 1.66/1.32 % ------ Schedule dynamic 5 is on
% 1.66/1.32
% 1.66/1.32 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.66/1.32
% 1.66/1.32
% 1.66/1.32 % ------
% 1.66/1.32 % Current options:
% 1.66/1.32 % ------
% 1.66/1.32
% 1.66/1.32
% 1.66/1.32 %
% 1.66/1.32
% 1.66/1.32 % ------ Proving...
% 1.66/1.32 %
% 1.66/1.32
% 1.66/1.32 % SZS status Unsatisfiable for theBenchmark.p
% 1.66/1.32
% 1.66/1.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.66/1.32
% 1.66/1.32
%------------------------------------------------------------------------------