%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL899+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 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 : Fri Sep 25 02:08:38 PM UTC 2026
% Result : Theorem 3.29s 1.19s
% Output : CNFRefutation 3.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 75 ( 46 unt; 2 def)
% Number of atoms : 130 ( 37 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 82 ( 41 ~; 33 |; 3 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 117 ( 0 sgn 116 !; 1 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : '+'(X0,X1) = '+'(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_02) ).
fof(f3,axiom,
! [X0] : '+'(X0,'0') = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_03) ).
fof(f4,axiom,
! [X0] : '>='(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_04) ).
fof(f5,axiom,
! [X0,X1,X2] :
( ( '>='(X1,X2)
& '>='(X0,X1) )
=> '>='(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_05) ).
fof(f6,axiom,
! [X0,X1] :
( ( '>='(X1,X0)
& '>='(X0,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_06) ).
fof(f7,axiom,
! [X0,X1,X2] :
( '>='('+'(X0,X1),X2)
<=> '>='(X1,'==>'(X0,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_07) ).
fof(f8,axiom,
! [X0] : '>='(X0,'0'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_08) ).
fof(f9,axiom,
! [X0,X1,X2] :
( '>='(X0,X1)
=> '>='('+'(X0,X2),'+'(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_09) ).
fof(f10,axiom,
! [X0,X1,X2] :
( '>='(X0,X1)
=> '>='('==>'(X1,X2),'==>'(X0,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_10) ).
fof(f12,axiom,
! [X0] : '+'(X0,'1') = '1',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_12) ).
fof(f13,axiom,
! [X0,X1] : '==>'('==>'(X0,X1),X1) = '==>'('==>'(X1,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_13) ).
fof(f14,conjecture,
! [X0] : '==>'('==>'(X0,'1'),'1') = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_14) ).
fof(f15,negated_conjecture,
~ ! [X0] : '==>'('==>'(X0,'1'),'1') = X0,
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ~ '>='(X1,X2)
| ~ '>='(X0,X1)
| '>='(X0,X2) ),
inference(ennf_transformation,[],[f5]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ~ '>='(X1,X2)
| ~ '>='(X0,X1)
| '>='(X0,X2) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ~ '>='(X1,X0)
| ~ '>='(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f6]) ).
fof(f19,plain,
! [X0,X1] :
( ~ '>='(X1,X0)
| ~ '>='(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ~ '>='(X0,X1)
| '>='('+'(X0,X2),'+'(X1,X2)) ),
inference(ennf_transformation,[],[f9]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ~ '>='(X0,X1)
| '>='('==>'(X1,X2),'==>'(X0,X2)) ),
inference(ennf_transformation,[],[f10]) ).
fof(f23,plain,
? [X0] : '==>'('==>'(X0,'1'),'1') != X0,
inference(ennf_transformation,[],[f15]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( ~ '>='('+'(X0,X1),X2)
| '>='(X1,'==>'(X0,X2)) )
& ( ~ '>='(X1,'==>'(X0,X2))
| '>='('+'(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f25,plain,
sK0 != '==>'('==>'(sK0,'1'),'1'),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f23]) ).
fof(f27,plain,
! [X0,X1] : '+'(X0,X1) = '+'(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f28,plain,
! [X0] : '+'(X0,'0') = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f29,plain,
! [X0] : '>='(X0,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f30,plain,
! [X2,X0,X1] :
( ~ '>='(X1,X2)
| ~ '>='(X0,X1)
| '>='(X0,X2) ),
inference(cnf_transformation,[],[f17]) ).
fof(f31,plain,
! [X0,X1] :
( ~ '>='(X1,X0)
| ~ '>='(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f19]) ).
fof(f32,plain,
! [X2,X0,X1] :
( ~ '>='('+'(X0,X1),X2)
| '>='(X1,'==>'(X0,X2)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f33,plain,
! [X2,X0,X1] :
( ~ '>='(X1,'==>'(X0,X2))
| '>='('+'(X0,X1),X2) ),
inference(cnf_transformation,[],[f24]) ).
fof(f34,plain,
! [X0] : '>='(X0,'0'),
inference(cnf_transformation,[],[f8]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ '>='(X0,X1)
| '>='('+'(X0,X2),'+'(X1,X2)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ '>='(X0,X1)
| '>='('==>'(X1,X2),'==>'(X0,X2)) ),
inference(cnf_transformation,[],[f21]) ).
fof(f38,plain,
! [X0] : '1' = '+'(X0,'1'),
inference(cnf_transformation,[],[f12]) ).
fof(f39,plain,
! [X0,X1] : '==>'('==>'(X0,X1),X1) = '==>'('==>'(X1,X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f40,plain,
sK0 != '==>'('==>'(sK0,'1'),'1'),
inference(cnf_transformation,[],[f25]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : '+'(X0,X1) = '+'(X1,X0),
inference(cnf_transformation,[],[f27]) ).
tcf(c_51,plain,
! [X0: $i] : '+'(X0,'0') = X0,
inference(cnf_transformation,[],[f28]) ).
tcf(c_52,plain,
! [X0: $i] : '>='(X0,X0),
inference(cnf_transformation,[],[f29]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( '>='(X0,X2)
| ~ '>='(X1,X2)
| ~ '>='(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ '>='(X1,X0)
| ~ '>='(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( '>='('+'(X1,X0),X2)
| ~ '>='(X0,'==>'(X1,X2)) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( '>='(X1,'==>'(X0,X2))
| ~ '>='('+'(X0,X1),X2) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_57,plain,
! [X0: $i] : '>='(X0,'0'),
inference(cnf_transformation,[],[f34]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( '>='('+'(X0,X2),'+'(X1,X2))
| ~ '>='(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( '>='('==>'(X1,X2),'==>'(X0,X2))
| ~ '>='(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_61,plain,
! [X0: $i] : '+'(X0,'1') = '1',
inference(cnf_transformation,[],[f38]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] : '==>'('==>'(X0,X1),X1) = '==>'('==>'(X1,X0),X0),
inference(cnf_transformation,[],[f39]) ).
tcf(c_63,negated_conjecture,
'==>'('==>'(sK0,'1'),'1') != sK0,
inference(cnf_transformation,[],[f40]) ).
tcf(c_148,plain,
'==>'('==>'('1',sK0),sK0) != sK0,
inference(demodulation,[status(thm)],[c_63,c_62]) ).
tcf(c_161,definition,
iPr_def_10 = '==>'('1',sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_162,definition,
iPr_def_11 = '==>'(iPr_def_10,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_163,plain,
iPr_def_11 != sK0,
inference(demodulation,[status(thm)],[c_148,c_161,c_162]) ).
tcf(c_344,plain,
! [X0: $i] : '+'('0',X0) = X0,
inference(superposition,[status(thm)],[c_50,c_51]) ).
tcf(c_345,plain,
! [X0: $i] : '+'('1',X0) = '1',
inference(superposition,[status(thm)],[c_50,c_61]) ).
tcf(c_355,plain,
! [X0: $i,X1: $i] :
( '>='(X1,X0)
| ~ '>='('0',X0) ),
inference(superposition,[status(thm)],[c_57,c_53]) ).
tcf(c_362,plain,
! [X0: $i,X1: $i] : '>='('+'(X0,'==>'(X0,X1)),X1),
inference(superposition,[status(thm)],[c_52,c_55]) ).
tcf(c_447,plain,
! [X0: $i,X1: $i] :
( '>='('+'(X0,X1),X1)
| ~ '>='(X0,'0') ),
inference(superposition,[status(thm)],[c_344,c_58]) ).
tcf(c_452,plain,
! [X0: $i,X1: $i] : '>='('+'(X0,X1),X1),
inference(forward_subsumption_resolution,[status(thm)],[c_447,c_57]) ).
tcf(c_467,plain,
! [X0: $i] : '>='('1',X0),
inference(superposition,[status(thm)],[c_345,c_452]) ).
tcf(c_469,plain,
! [X0: $i,X1: $i] : '>='(X0,'==>'(X1,X0)),
inference(superposition,[status(thm)],[c_452,c_56]) ).
tcf(c_542,plain,
! [X0: $i] : '>='('==>'('0',X0),X0),
inference(superposition,[status(thm)],[c_344,c_362]) ).
tcf(c_659,plain,
! [X0: $i] :
( '>='('==>'(X0,sK0),iPr_def_10)
| ~ '>='('1',X0) ),
inference(superposition,[status(thm)],[c_161,c_59]) ).
tcf(c_665,plain,
! [X0: $i] : '>='('==>'(X0,sK0),iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_659,c_467]) ).
tcf(c_791,plain,
! [X0: $i] :
( ( X0 = '0' )
| ~ '>='('0',X0) ),
inference(superposition,[status(thm)],[c_57,c_54]) ).
tcf(c_804,plain,
! [X0: $i] :
( ( '==>'('0',X0) = X0 )
| ~ '>='(X0,'==>'('0',X0)) ),
inference(superposition,[status(thm)],[c_542,c_54]) ).
tcf(c_813,plain,
! [X0: $i] : '==>'('0',X0) = X0,
inference(forward_subsumption_resolution,[status(thm)],[c_804,c_469]) ).
tcf(c_1134,plain,
! [X0: $i] : '>='('==>'('==>'(sK0,X0),X0),iPr_def_10),
inference(superposition,[status(thm)],[c_62,c_665]) ).
tcf(c_4001,plain,
! [X0: $i] : '==>'(X0,'0') = '0',
inference(superposition,[status(thm)],[c_469,c_791]) ).
tcf(c_4098,plain,
'>='('0',iPr_def_10),
inference(superposition,[status(thm)],[c_4001,c_1134]) ).
tcf(c_4141,plain,
! [X0: $i] : '>='(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_4098,c_355]) ).
tcf(c_4146,plain,
'0' = iPr_def_10,
inference(superposition,[status(thm)],[c_4141,c_791]) ).
tcf(c_4157,plain,
! [X0: $i] : '==>'(iPr_def_10,X0) = X0,
inference(demodulation,[status(thm)],[c_813,c_4146]) ).
tcf(c_4195,plain,
sK0 = iPr_def_11,
inference(demodulation,[status(thm)],[c_162,c_4157]) ).
tcf(c_4227,plain,
iPr_def_11 != iPr_def_11,
inference(demodulation,[status(thm)],[c_163,c_4195]) ).
tcf(c_4228,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_4227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL899+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 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 : Thu Sep 24 00:39:48 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.43 % Proving...
% 3.29/1.19 % SZS status Started for theBenchmark.p
% 3.29/1.19 % SZS status Theorem for theBenchmark.p
% 3.29/1.19
% 3.29/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.29/1.19
% 3.29/1.19 % ------ iProver source info
% 3.29/1.19
% 3.29/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 3.29/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.29/1.19 % git: non_committed_changes: false
% 3.29/1.19
% 3.29/1.19 % ------ Parsing...
% 3.29/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.29/1.19
% 3.29/1.19 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.29/1.19
% 3.29/1.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.29/1.19
% 3.29/1.19 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.29/1.19 % ------ Proving...
% 3.29/1.19 % ------ Problem Properties
% 3.29/1.19
% 3.29/1.19 %
% 3.29/1.19 % clauses 17
% 3.29/1.19 % conjectures 0
% 3.29/1.19 % EPR 5
% 3.29/1.19 % Horn 17
% 3.29/1.19 % unary 10
% 3.29/1.19 % binary 5
% 3.29/1.19 % lits 26
% 3.29/1.19 % lits eq 9
% 3.29/1.19 % fd_pure 0
% 3.29/1.19 % fd_pseudo 0
% 3.29/1.19 % fd_cond 0
% 3.29/1.19 % fd_pseudo_cond 1
% 3.29/1.19 % AC symbols 1
% 3.29/1.19
% 3.29/1.19 % ------ Schedule dynamic 5 is on
% 3.29/1.19
% 3.29/1.19 % ------ no conjectures: strip conj schedule
% 3.29/1.19
% 3.29/1.19 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.29/1.19
% 3.29/1.19
% 3.29/1.19 % ------
% 3.29/1.19 % Current options:
% 3.29/1.19 % ------
% 3.29/1.19
% 3.29/1.19
% 3.29/1.19 %
% 3.29/1.19
% 3.29/1.19 % ------ Proving...
% 3.29/1.19 %
% 3.29/1.19
% 3.29/1.19 % SZS status Theorem for theBenchmark.p
% 3.29/1.19
% 3.29/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.29/1.19
% 3.29/1.19
%------------------------------------------------------------------------------