%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL902+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 : n011.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 02:08:39 PM UTC 2026
% Result : Theorem 4.16s 1.17s
% Output : CNFRefutation 4.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 66 ( 46 unt; 2 def)
% Number of atoms : 128 ( 35 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 66 ( 33 ~; 27 |; 3 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 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 : 84 ( 0 sgn 83 !; 1 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] : '+'('+'(X0,X1),X2) = '+'(X0,'+'(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_01) ).
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(f12,axiom,
! [X0] : '+'(X0,'1') = '1',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_12) ).
fof(f13,axiom,
! [X0] : '==>'('==>'('==>'(X0,'1'),X0),X0) = '0',
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(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(f26,plain,
! [X2,X0,X1] : '+'('+'(X0,X1),X2) = '+'(X0,'+'(X1,X2)),
inference(cnf_transformation,[],[f1]) ).
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(f38,plain,
! [X0] : '1' = '+'(X0,'1'),
inference(cnf_transformation,[],[f12]) ).
fof(f39,plain,
! [X0] : '0' = '==>'('==>'('==>'(X0,'1'),X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f40,plain,
sK0 != '==>'('==>'(sK0,'1'),'1'),
inference(cnf_transformation,[],[f25]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] : '+'('+'(X0,X1),X2) = '+'(X0,'+'(X1,X2)),
inference(cnf_transformation,[],[f26]) ).
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_61,plain,
! [X0: $i] : '+'(X0,'1') = '1',
inference(cnf_transformation,[],[f38]) ).
tcf(c_62,plain,
! [X0: $i] : '==>'('==>'('==>'(X0,'1'),X0),X0) = '0',
inference(cnf_transformation,[],[f39]) ).
tcf(c_63,negated_conjecture,
'==>'('==>'(sK0,'1'),'1') != sK0,
inference(cnf_transformation,[],[f40]) ).
tcf(c_160,definition,
iPr_def_10 = '==>'(sK0,'1'),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_161,definition,
iPr_def_11 = '==>'(iPr_def_10,'1'),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_162,negated_conjecture,
iPr_def_11 != sK0,
inference(demodulation,[status(thm)],[c_63,c_160,c_161]) ).
tcf(c_343,plain,
! [X0: $i] : '+'('0',X0) = X0,
inference(superposition,[status(thm)],[c_50,c_51]) ).
tcf(c_344,plain,
! [X0: $i] : '+'('1',X0) = '1',
inference(superposition,[status(thm)],[c_50,c_61]) ).
tcf(c_351,plain,
'==>'('==>'(iPr_def_10,sK0),sK0) = '0',
inference(superposition,[status(thm)],[c_160,c_62]) ).
tcf(c_365,plain,
! [X0: $i,X1: $i] : '>='('+'(X0,'==>'(X0,X1)),X1),
inference(superposition,[status(thm)],[c_52,c_55]) ).
tcf(c_424,plain,
! [X0: $i] : '>='('1',X0),
inference(superposition,[status(thm)],[c_344,c_365]) ).
tcf(c_426,plain,
'>='('+'(sK0,iPr_def_10),'1'),
inference(superposition,[status(thm)],[c_160,c_365]) ).
tcf(c_427,plain,
'>='('+'(iPr_def_10,iPr_def_11),'1'),
inference(superposition,[status(thm)],[c_161,c_365]) ).
tcf(c_431,plain,
'>='('+'(iPr_def_10,sK0),'1'),
inference(theory_normalisation,[status(thm)],[c_426,c_49,c_50]) ).
tcf(c_438,plain,
( ( iPr_def_11 = sK0 )
| ~ '>='(iPr_def_11,sK0)
| ~ '>='(sK0,iPr_def_11) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_457,plain,
! [X0: $i] :
( '>='('+'(iPr_def_10,iPr_def_11),X0)
| ~ '>='('1',X0) ),
inference(superposition,[status(thm)],[c_427,c_53]) ).
tcf(c_460,plain,
! [X0: $i] : '>='('+'(iPr_def_10,iPr_def_11),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_457,c_424]) ).
tcf(c_461,plain,
! [X0: $i] :
( '>='('+'(iPr_def_10,sK0),X0)
| ~ '>='('1',X0) ),
inference(superposition,[status(thm)],[c_431,c_53]) ).
tcf(c_464,plain,
! [X0: $i] : '>='('+'(iPr_def_10,sK0),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_461,c_424]) ).
tcf(c_466,plain,
! [X0: $i] : '>='(iPr_def_11,'==>'(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_460,c_56]) ).
tcf(c_479,plain,
! [X0: $i] : '>='(sK0,'==>'(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_464,c_56]) ).
tcf(c_489,plain,
'>='(sK0,iPr_def_11),
inference(superposition,[status(thm)],[c_161,c_479]) ).
tcf(c_505,plain,
'>='('+'('==>'(iPr_def_10,sK0),'0'),sK0),
inference(superposition,[status(thm)],[c_351,c_365]) ).
tcf(c_506,plain,
'>='('+'('0','==>'(iPr_def_10,sK0)),sK0),
inference(theory_normalisation,[status(thm)],[c_505,c_49,c_50]) ).
tcf(c_865,plain,
'>='('==>'(iPr_def_10,sK0),sK0),
inference(demodulation,[status(thm)],[c_506,c_343]) ).
tcf(c_965,plain,
( ( '==>'(iPr_def_10,sK0) = sK0 )
| ~ '>='(sK0,'==>'(iPr_def_10,sK0)) ),
inference(superposition,[status(thm)],[c_865,c_54]) ).
tcf(c_972,plain,
'==>'(iPr_def_10,sK0) = sK0,
inference(forward_subsumption_resolution,[status(thm)],[c_965,c_479]) ).
tcf(c_1104,plain,
'>='(iPr_def_11,sK0),
inference(superposition,[status(thm)],[c_972,c_466]) ).
tcf(c_1111,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1104,c_489,c_438,c_162]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL902+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n011.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 00:39:57 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 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
% 0.14/0.42 % Proving...
% 4.16/1.17 % SZS status Started for theBenchmark.p
% 4.16/1.17 % SZS status Theorem for theBenchmark.p
% 4.16/1.17
% 4.16/1.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.16/1.17
% 4.16/1.17 % ------ iProver source info
% 4.16/1.17
% 4.16/1.17 % git: date: 2026-07-19 20:42:38 +0200
% 4.16/1.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.16/1.17 % git: non_committed_changes: false
% 4.16/1.17
% 4.16/1.17 % ------ Parsing...
% 4.16/1.17 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.16/1.17
% 4.16/1.17 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 4.16/1.17
% 4.16/1.17 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.16/1.17
% 4.16/1.17 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.16/1.17 % ------ Proving...
% 4.16/1.17 % ------ Problem Properties
% 4.16/1.17
% 4.16/1.17 %
% 4.16/1.17 % clauses 17
% 4.16/1.17 % conjectures 1
% 4.16/1.17 % EPR 5
% 4.16/1.17 % Horn 17
% 4.16/1.17 % unary 10
% 4.16/1.17 % binary 5
% 4.16/1.17 % lits 26
% 4.16/1.17 % lits eq 9
% 4.16/1.17 % fd_pure 0
% 4.16/1.17 % fd_pseudo 0
% 4.16/1.17 % fd_cond 0
% 4.16/1.17 % fd_pseudo_cond 1
% 4.16/1.17 % AC symbols 1
% 4.16/1.17
% 4.16/1.17 % ------ Schedule dynamic 5 is on
% 4.16/1.17
% 4.16/1.17 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.16/1.17
% 4.16/1.17
% 4.16/1.17 % ------
% 4.16/1.17 % Current options:
% 4.16/1.17 % ------
% 4.16/1.17
% 4.16/1.17
% 4.16/1.17 %
% 4.16/1.17
% 4.16/1.17 % ------ Proving...
% 4.16/1.17 %
% 4.16/1.17
% 4.16/1.17 % SZS status Theorem for theBenchmark.p
% 4.16/1.17
% 4.16/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.16/1.17
% 4.16/1.17
%------------------------------------------------------------------------------