%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET794+4 : 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 : n018.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 02:48:35 PM UTC 2026
% Result : Theorem 1.84s 1.26s
% Output : CNFRefutation 1.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 59 ( 18 unt; 1 def)
% Number of atoms : 193 ( 26 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 203 ( 82 ~; 82 |; 25 &)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 2 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 120 ( 0 sgn 112 !; 8 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( total_order(X0,X1)
<=> ( ! [X2,X3] :
( ( member(X3,X1)
& member(X2,X1) )
=> ( apply(X0,X3,X2)
| apply(X0,X2,X3) ) )
& order(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',total_order) ).
fof(f6,axiom,
! [X0,X1,X2] :
( least(X2,X0,X1)
<=> ( ! [X3] :
( member(X3,X1)
=> apply(X0,X2,X3) )
& member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',least) ).
fof(f8,axiom,
! [X0,X1,X2] :
( min(X2,X0,X1)
<=> ( ! [X3] :
( ( apply(X0,X3,X2)
& member(X3,X1) )
=> X2 = X3 )
& member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',min) ).
fof(f11,conjecture,
! [X0,X1,X2] :
( ( min(X2,X0,X1)
& total_order(X0,X1) )
=> least(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV6) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X2] :
( ( min(X2,X0,X1)
& total_order(X0,X1) )
=> least(X2,X0,X1) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f14,plain,
! [X0,X1,X2] :
( min(X2,X0,X1)
=> ( ! [X3] :
( ( apply(X0,X3,X2)
& member(X3,X1) )
=> X2 = X3 )
& member(X2,X1) ) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( member(X3,X1)
=> apply(X0,X2,X3) )
& member(X2,X1) )
=> least(X2,X0,X1) ),
inference(unused_predicate_definition_removal,[],[f6]) ).
fof(f16,plain,
! [X0,X1] :
( total_order(X0,X1)
=> ( ! [X2,X3] :
( ( member(X3,X1)
& member(X2,X1) )
=> ( apply(X0,X3,X2)
| apply(X0,X2,X3) ) )
& order(X0,X1) ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f20,plain,
! [X0,X1] :
( ~ total_order(X0,X1)
| ( ! [X2,X3] :
( ~ member(X3,X1)
| ~ member(X2,X1)
| apply(X0,X3,X2)
| apply(X0,X2,X3) )
& order(X0,X1) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f21,plain,
! [X0,X1] :
( ~ total_order(X0,X1)
| ( ! [X2,X3] :
( ~ member(X3,X1)
| ~ member(X2,X1)
| apply(X0,X3,X2)
| apply(X0,X2,X3) )
& order(X0,X1) ) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ? [X3] :
( member(X3,X1)
& ~ apply(X0,X2,X3) )
| ~ member(X2,X1)
| least(X2,X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ? [X3] :
( member(X3,X1)
& ~ apply(X0,X2,X3) )
| ~ member(X2,X1)
| least(X2,X0,X1) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ~ min(X2,X0,X1)
| ( ! [X3] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1)
| X2 = X3 )
& member(X2,X1) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ~ min(X2,X0,X1)
| ( ! [X3] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1)
| X2 = X3 )
& member(X2,X1) ) ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
? [X0,X1,X2] :
( min(X2,X0,X1)
& total_order(X0,X1)
& ~ least(X2,X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f27,plain,
? [X0,X1,X2] :
( min(X2,X0,X1)
& total_order(X0,X1)
& ~ least(X2,X0,X1) ),
inference(flattening,[],[f26]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( member(sK0(X0,X1,X2),X1)
& ~ apply(X0,X2,sK0(X0,X1,X2)) )
| ~ member(X2,X1)
| least(X2,X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f23]) ).
fof(f29,plain,
( min(sK3,sK1,sK2)
& total_order(sK1,sK2)
& ~ least(sK3,sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f27]) ).
fof(f33,plain,
! [X2,X3,X0,X1] :
( ~ total_order(X0,X1)
| ~ member(X3,X1)
| ~ member(X2,X1)
| apply(X0,X3,X2)
| apply(X0,X2,X3) ),
inference(cnf_transformation,[],[f21]) ).
fof(f35,plain,
! [X2,X0,X1] :
( member(sK0(X0,X1,X2),X1)
| ~ member(X2,X1)
| least(X2,X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ apply(X0,X2,sK0(X0,X1,X2))
| ~ member(X2,X1)
| least(X2,X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f37,plain,
! [X2,X3,X0,X1] :
( ~ min(X2,X0,X1)
| ~ apply(X0,X3,X2)
| ~ member(X3,X1)
| X2 = X3 ),
inference(cnf_transformation,[],[f25]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ min(X2,X0,X1)
| member(X2,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f39,plain,
min(sK3,sK1,sK2),
inference(cnf_transformation,[],[f29]) ).
fof(f40,plain,
total_order(sK1,sK2),
inference(cnf_transformation,[],[f29]) ).
fof(f41,plain,
~ least(sK3,sK1,sK2),
inference(cnf_transformation,[],[f29]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X3,X2,X0)
| apply(X3,X0,X2)
| ~ total_order(X3,X1)
| ~ member(X2,X1)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( least(X1,X0,X2)
| ~ member(X1,X2)
| ~ apply(X0,X1,sK0(X0,X2,X1)) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( least(X0,X2,X1)
| member(sK0(X2,X1,X0),X1)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ min(X0,X1,X2) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ~ member(X1,X3)
| ~ min(X2,X0,X3)
| ~ apply(X0,X1,X2) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_58,negated_conjecture,
~ least(sK3,sK1,sK2),
inference(cnf_transformation,[],[f41]) ).
tcf(c_59,negated_conjecture,
total_order(sK1,sK2),
inference(cnf_transformation,[],[f40]) ).
tcf(c_60,negated_conjecture,
min(sK3,sK1,sK2),
inference(cnf_transformation,[],[f39]) ).
tcf(c_221,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ member(X1,X2)
| ~ apply(X0,X1,sK0(X0,X2,X1))
| ( X2 != sK2 )
| ( X1 != sK3 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_58]) ).
tcf(c_222,plain,
( ~ member(sK3,sK2)
| ~ apply(sK1,sK3,sK0(sK1,sK2,sK3)) ),
inference(unflattening,[status(thm)],[c_221]) ).
tcf(c_229,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK0(X2,X1,X0),X1)
| ~ member(X0,X1)
| ( X2 != sK1 )
| ( X1 != sK2 )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_58]) ).
tcf(c_230,plain,
( member(sK0(sK1,sK2,sK3),sK2)
| ~ member(sK3,sK2) ),
inference(unflattening,[status(thm)],[c_229]) ).
tcf(c_241,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ( X2 != sK2 )
| ( X1 != sK1 )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_60]) ).
tcf(c_242,plain,
member(sK3,sK2),
inference(unflattening,[status(thm)],[c_241]) ).
tcf(c_246,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ~ member(X3,X2)
| ~ apply(X0,X3,X1)
| ( X2 != sK2 )
| ( X1 != sK3 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_57,c_60]) ).
tcf(c_247,plain,
! [X0: $i] :
( ( sK3 = X0 )
| ~ member(X0,sK2)
| ~ apply(sK1,X0,sK3) ),
inference(unflattening,[status(thm)],[c_246]) ).
tcf(c_259,plain,
~ apply(sK1,sK3,sK0(sK1,sK2,sK3)),
inference(backward_subsumption_resolution,[status(thm)],[c_222,c_242]) ).
tcf(c_260,plain,
member(sK0(sK1,sK2,sK3),sK2),
inference(backward_subsumption_resolution,[status(thm)],[c_230,c_242]) ).
tcf(c_269,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X1,X3,X2)
| apply(X1,X2,X3)
| ~ member(X3,X0)
| ~ member(X2,X0)
| ( X1 != sK1 )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_59]) ).
tcf(c_270,plain,
! [X0: $i,X1: $i] :
( apply(sK1,X1,X0)
| apply(sK1,X0,X1)
| ~ member(X1,sK2)
| ~ member(X0,sK2) ),
inference(unflattening,[status(thm)],[c_269]) ).
tcf(c_438,definition,
iPr_def_10 = sK0(sK1,sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_442,plain,
! [X0: $i,X1: $i] :
( apply(sK1,X1,X0)
| apply(sK1,X0,X1)
| ~ member(X1,sK2)
| ~ member(X0,sK2) ),
inference(demodulation,[status(thm)],[c_270]) ).
tcf(c_443,plain,
member(iPr_def_10,sK2),
inference(demodulation,[status(thm)],[c_260,c_438]) ).
tcf(c_444,plain,
~ apply(sK1,sK3,iPr_def_10),
inference(demodulation,[status(thm)],[c_259]) ).
tcf(c_445,plain,
! [X0: $i] :
( ( sK3 = X0 )
| ~ member(X0,sK2)
| ~ apply(sK1,X0,sK3) ),
inference(demodulation,[status(thm)],[c_247]) ).
tcf(c_446,plain,
member(sK3,sK2),
inference(demodulation,[status(thm)],[c_242]) ).
tcf(c_642,plain,
( apply(sK1,iPr_def_10,sK3)
| ~ member(iPr_def_10,sK2)
| ~ member(sK3,sK2) ),
inference(superposition,[status(thm)],[c_442,c_444]) ).
tcf(c_644,plain,
apply(sK1,iPr_def_10,sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_642,c_443,c_446]) ).
tcf(c_645,plain,
( ( sK3 = iPr_def_10 )
| ~ member(iPr_def_10,sK2) ),
inference(superposition,[status(thm)],[c_644,c_445]) ).
tcf(c_646,plain,
sK3 = iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_645,c_443]) ).
tcf(c_647,plain,
apply(sK1,iPr_def_10,iPr_def_10),
inference(demodulation,[status(thm)],[c_644,c_646]) ).
tcf(c_648,plain,
~ apply(sK1,iPr_def_10,iPr_def_10),
inference(demodulation,[status(thm)],[c_444,c_646]) ).
tcf(c_654,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_647,c_648]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET794+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 12:00:34 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 1.84/1.26 % SZS status Started for theBenchmark.p
% 1.84/1.26 % SZS status Theorem for theBenchmark.p
% 1.84/1.26
% 1.84/1.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.84/1.26
% 1.84/1.26 % ------ iProver source info
% 1.84/1.26
% 1.84/1.26 % git: date: 2026-07-19 20:42:38 +0200
% 1.84/1.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.84/1.26 % git: non_committed_changes: false
% 1.84/1.26
% 1.84/1.26 % ------ Parsing...
% 1.84/1.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.84/1.26
% 1.84/1.26 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 1.84/1.26
% 1.84/1.26 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.84/1.26
% 1.84/1.26 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.84/1.26 % ------ Proving...
% 1.84/1.26 % ------ Problem Properties
% 1.84/1.26
% 1.84/1.26 %
% 1.84/1.26 % clauses 9
% 1.84/1.26 % conjectures 0
% 1.84/1.26 % EPR 8
% 1.84/1.26 % Horn 8
% 1.84/1.26 % unary 4
% 1.84/1.26 % binary 1
% 1.84/1.26 % lits 24
% 1.84/1.27 % lits eq 3
% 1.84/1.27 % fd_pure 0
% 1.84/1.27 % fd_pseudo 0
% 1.84/1.27 % fd_cond 1
% 1.84/1.27 % fd_pseudo_cond 1
% 1.84/1.27 % AC symbols 0
% 1.84/1.27
% 1.84/1.27 % ------ Schedule dynamic 5 is on
% 1.84/1.27
% 1.84/1.27 % ------ no conjectures: strip conj schedule
% 1.84/1.27
% 1.84/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 1.84/1.27
% 1.84/1.27
% 1.84/1.27 % ------
% 1.84/1.27 % Current options:
% 1.84/1.27 % ------
% 1.84/1.27
% 1.84/1.27
% 1.84/1.27 %
% 1.84/1.27
% 1.84/1.27 % ------ Proving...
% 1.84/1.27 %
% 1.84/1.27
% 1.84/1.27 % SZS status Theorem for theBenchmark.p
% 1.84/1.27
% 1.84/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.84/1.27
% 1.84/1.27
%------------------------------------------------------------------------------