%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET616+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n008.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 02:47:34 PM UTC 2026
% Result : Theorem 2.47s 6.29s
% Output : CNFRefutation 2.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 52 ( 14 unt; 2 def)
% Number of atoms : 138 ( 25 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 131 ( 55 ~; 51 |; 18 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 79 ( 0 sgn 75 !; 4 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( ~ member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f5,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f7,conjecture,
! [X0,X1] :
( difference(X0,X1) = difference(X1,X0)
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th90) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( difference(X0,X1) = difference(X1,X0)
=> X0 = X1 ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f10,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f11,plain,
? [X0,X1] :
( difference(X0,X1) = difference(X1,X0)
& X0 != X1 ),
inference(ennf_transformation,[],[f8]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( ~ member(X2,difference(X0,X1))
| ( ~ member(X2,X1)
& member(X2,X0) ) )
& ( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( ~ member(X2,difference(X0,X1))
| ( ~ member(X2,X1)
& member(X2,X0) ) )
& ( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f17,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f16]) ).
fof(f21,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f22,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK2(X0,X1),X0)
& ~ member(sK2(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f22]) ).
fof(f24,plain,
( difference(sK3,sK4) = difference(sK4,sK3)
& sK3 != sK4 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f11]) ).
fof(f27,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f28,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f32,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f17]) ).
fof(f38,plain,
! [X0,X1] :
( member(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f39,plain,
! [X0,X1] :
( ~ member(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f41,plain,
difference(sK3,sK4) = difference(sK4,sK3),
inference(cnf_transformation,[],[f24]) ).
fof(f42,plain,
sK3 != sK4,
inference(cnf_transformation,[],[f24]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,difference(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_63,negated_conjecture,
sK3 != sK4,
inference(cnf_transformation,[],[f42]) ).
tcf(c_64,negated_conjecture,
difference(sK3,sK4) = difference(sK4,sK3),
inference(cnf_transformation,[],[f41]) ).
tcf(c_323,definition,
iPr_def_10 = difference(sK3,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_324,definition,
iPr_def_11 = difference(sK4,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_325,negated_conjecture,
iPr_def_10 = iPr_def_11,
inference(demodulation,[status(thm)],[c_64,c_324,c_323]) ).
tcf(c_326,negated_conjecture,
sK3 != sK4,
inference(demodulation,[status(thm)],[c_63]) ).
tcf(c_517,plain,
difference(sK4,sK3) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_324,c_325]) ).
tcf(c_525,plain,
! [X0: $i] :
( member(X0,sK3)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_323,c_52]) ).
tcf(c_550,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| member(X0,sK4)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_323,c_51]) ).
tcf(c_551,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| member(X0,sK3)
| ~ member(X0,sK4) ),
inference(superposition,[status(thm)],[c_517,c_51]) ).
tcf(c_577,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_10)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_517,c_53]) ).
tcf(c_609,plain,
! [X0: $i] : ~ member(X0,iPr_def_10),
inference(global_subsumption_just,[status(thm)],[c_525,c_525,c_577]) ).
tcf(c_624,plain,
! [X0: $i] :
( ~ member(X0,sK4)
| member(X0,sK3) ),
inference(global_subsumption_just,[status(thm)],[c_551,c_525,c_551,c_577]) ).
tcf(c_625,plain,
! [X0: $i] :
( member(X0,sK3)
| ~ member(X0,sK4) ),
inference(renaming,[status(thm)],[c_624]) ).
tcf(c_631,plain,
! [X0: $i] :
( subset(sK4,X0)
| member(sK2(sK4,X0),sK3) ),
inference(superposition,[status(thm)],[c_60,c_625]) ).
tcf(c_640,plain,
subset(sK4,sK3),
inference(superposition,[status(thm)],[c_631,c_59]) ).
tcf(c_644,plain,
( ( sK3 = sK4 )
| ~ subset(sK3,sK4) ),
inference(superposition,[status(thm)],[c_640,c_54]) ).
tcf(c_645,plain,
~ subset(sK3,sK4),
inference(forward_subsumption_resolution,[status(thm)],[c_644,c_326]) ).
tcf(c_685,plain,
! [X0: $i] :
( ~ member(X0,sK3)
| member(X0,sK4) ),
inference(global_subsumption_just,[status(thm)],[c_550,c_550,c_609]) ).
tcf(c_686,plain,
! [X0: $i] :
( member(X0,sK4)
| ~ member(X0,sK3) ),
inference(renaming,[status(thm)],[c_685]) ).
tcf(c_692,plain,
! [X0: $i] :
( subset(sK3,X0)
| member(sK2(sK3,X0),sK4) ),
inference(superposition,[status(thm)],[c_60,c_686]) ).
tcf(c_888,plain,
subset(sK3,sK4),
inference(superposition,[status(thm)],[c_692,c_59]) ).
tcf(c_890,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_888,c_645]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET616+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/5.38 % Computer : n008.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Thu Sep 24 11:29:16 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 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
% 0.14/5.43
% 0.14/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.43
% 0.14/5.43 % Detected problem language: tptp
% 0.14/5.44 % Proving...
% 2.47/6.29 % SZS status Started for theBenchmark.p
% 2.47/6.29 % SZS status Theorem for theBenchmark.p
% 2.47/6.29
% 2.47/6.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.47/6.29
% 2.47/6.29 % ------ iProver source info
% 2.47/6.29
% 2.47/6.29 % git: date: 2026-07-19 20:42:38 +0200
% 2.47/6.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.47/6.29 % git: non_committed_changes: false
% 2.47/6.29
% 2.47/6.29 % ------ Parsing...
% 2.47/6.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.47/6.29
% 2.47/6.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.47/6.29
% 2.47/6.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.47/6.29
% 2.47/6.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.47/6.29 % ------ Proving...
% 2.47/6.29 % ------ Problem Properties
% 2.47/6.29
% 2.47/6.29 %
% 2.47/6.29 % clauses 16
% 2.47/6.29 % conjectures 2
% 2.47/6.29 % EPR 5
% 2.47/6.29 % Horn 12
% 2.47/6.29 % unary 5
% 2.47/6.29 % binary 4
% 2.47/6.29 % lits 34
% 2.47/6.29 % lits eq 9
% 2.47/6.29 % fd_pure 0
% 2.47/6.29 % fd_pseudo 0
% 2.47/6.29 % fd_cond 0
% 2.47/6.29 % fd_pseudo_cond 5
% 2.47/6.29 % AC symbols 0
% 2.47/6.29
% 2.47/6.29 % ------ Schedule dynamic 5 is on
% 2.47/6.29
% 2.47/6.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.47/6.29
% 2.47/6.29
% 2.47/6.29 % ------
% 2.47/6.29 % Current options:
% 2.47/6.29 % ------
% 2.47/6.29
% 2.47/6.29
% 2.47/6.29 %
% 2.47/6.29
% 2.47/6.29 % ------ Proving...
% 2.47/6.29 %
% 2.47/6.29
% 2.47/6.29 % SZS status Theorem for theBenchmark.p
% 2.47/6.29
% 2.47/6.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.47/6.29
% 2.47/6.29
%------------------------------------------------------------------------------