%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET624+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 : n005.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 02:47:36 PM UTC 2026
% Result : Theorem 3.91s 1.18s
% Output : CNFRefutation 3.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 58 ( 4 unt; 1 def)
% Number of atoms : 185 ( 1 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 179 ( 74 ~; 82 |; 17 &)
% ( 4 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 5 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 : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 94 ( 0 sgn 82 !; 12 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(f2,axiom,
! [X0,X1] :
( intersect(X0,X1)
<=> ? [X2] :
( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).
fof(f4,axiom,
! [X0,X1] :
( intersect(X0,X1)
=> intersect(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_intersect) ).
fof(f6,conjecture,
! [X0,X1,X2] :
( intersect(X0,union(X1,X2))
<=> ( intersect(X0,X2)
| intersect(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_intersect_with_union) ).
fof(f7,negated_conjecture,
~ ! [X0,X1,X2] :
( intersect(X0,union(X1,X2))
<=> ( intersect(X0,X2)
| intersect(X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| intersect(X1,X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f9,plain,
? [X0,X1,X2] :
( intersect(X0,union(X1,X2))
<~> ( intersect(X0,X2)
| intersect(X0,X1) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f10,plain,
! [X0,X1,X2] :
( ( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) )
& ( ( ~ member(X2,X1)
& ~ member(X2,X0) )
| member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f11,plain,
! [X0,X1,X2] :
( ( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) )
& ( ( ~ member(X2,X1)
& ~ member(X2,X0) )
| member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f10]) ).
fof(f12,plain,
! [X0,X1] :
( ( ~ intersect(X0,X1)
| ? [X2] :
( member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) )
| intersect(X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f13,plain,
! [X0,X1] :
( ( ~ intersect(X0,X1)
| ? [X3] :
( member(X3,X1)
& member(X3,X0) ) )
& ( ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) )
| intersect(X0,X1) ) ),
inference(rectify,[],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ( ~ intersect(X0,X1)
| ( member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) )
| intersect(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f13]) ).
fof(f18,plain,
? [X0,X1,X2] :
( ( intersect(X0,union(X1,X2))
| intersect(X0,X2)
| intersect(X0,X1) )
& ( ~ intersect(X0,union(X1,X2))
| ( ~ intersect(X0,X2)
& ~ intersect(X0,X1) ) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f19,plain,
? [X0,X1,X2] :
( ( intersect(X0,union(X1,X2))
| intersect(X0,X2)
| intersect(X0,X1) )
& ( ~ intersect(X0,union(X1,X2))
| ( ~ intersect(X0,X2)
& ~ intersect(X0,X1) ) ) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
( ( intersect(sK2,union(sK3,sK4))
| intersect(sK2,sK4)
| intersect(sK2,sK3) )
& ( ~ intersect(sK2,union(sK3,sK4))
| ( ~ intersect(sK2,sK4)
& ~ intersect(sK2,sK3) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f19]) ).
fof(f21,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) ),
inference(cnf_transformation,[],[f11]) ).
fof(f22,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f11]) ).
fof(f23,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f11]) ).
fof(f24,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f25,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f26,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| intersect(X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f28,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| intersect(X1,X0) ),
inference(cnf_transformation,[],[f8]) ).
fof(f33,plain,
( intersect(sK2,union(sK3,sK4))
| intersect(sK2,sK4)
| intersect(sK2,sK3) ),
inference(cnf_transformation,[],[f20]) ).
fof(f34,plain,
( ~ intersect(sK2,union(sK3,sK4))
| ~ intersect(sK2,sK4) ),
inference(cnf_transformation,[],[f20]) ).
fof(f35,plain,
( ~ intersect(sK2,union(sK3,sK4))
| ~ intersect(sK2,sK3) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( intersect(X1,X2)
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( member(sK0(X0,X1),X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( member(sK0(X0,X1),X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( intersect(X1,X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_59,negated_conjecture,
( ~ intersect(sK2,sK3)
| ~ intersect(sK2,union(sK3,sK4)) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_60,negated_conjecture,
( ~ intersect(sK2,sK4)
| ~ intersect(sK2,union(sK3,sK4)) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_61,negated_conjecture,
( intersect(sK2,sK4)
| intersect(sK2,sK3)
| intersect(sK2,union(sK3,sK4)) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_191,definition,
iPr_def_10 = union(sK3,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_192,negated_conjecture,
( intersect(sK2,iPr_def_10)
| intersect(sK2,sK4)
| intersect(sK2,sK3) ),
inference(demodulation,[status(thm)],[c_61,c_191]) ).
tcf(c_193,negated_conjecture,
( ~ intersect(sK2,iPr_def_10)
| ~ intersect(sK2,sK4) ),
inference(demodulation,[status(thm)],[c_60]) ).
tcf(c_194,negated_conjecture,
( ~ intersect(sK2,iPr_def_10)
| ~ intersect(sK2,sK3) ),
inference(demodulation,[status(thm)],[c_59]) ).
tcf(c_423,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_191,c_49]) ).
tcf(c_433,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,sK4) ),
inference(superposition,[status(thm)],[c_191,c_50]) ).
tcf(c_453,plain,
! [X0: $i,X1: $i,X2: $i] :
( intersect(X0,X2)
| ~ intersect(X0,X1)
| ~ member(sK0(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_53,c_52]) ).
tcf(c_454,plain,
! [X0: $i,X1: $i,X2: $i] :
( intersect(X1,X2)
| ~ intersect(X0,X1)
| ~ member(sK0(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_54,c_52]) ).
tcf(c_480,plain,
! [X0: $i] :
( member(X0,sK4)
| member(X0,sK3)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_191,c_51]) ).
tcf(c_498,plain,
! [X0: $i] :
( member(sK0(X0,sK3),iPr_def_10)
| ~ intersect(X0,sK3) ),
inference(superposition,[status(thm)],[c_54,c_423]) ).
tcf(c_510,plain,
! [X0: $i] :
( member(sK0(X0,sK4),iPr_def_10)
| ~ intersect(X0,sK4) ),
inference(superposition,[status(thm)],[c_54,c_433]) ).
tcf(c_559,plain,
! [X0: $i] :
( member(sK0(iPr_def_10,X0),sK4)
| member(sK0(iPr_def_10,X0),sK3)
| ~ intersect(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_53,c_480]) ).
tcf(c_693,plain,
( intersect(iPr_def_10,sK2)
| ~ intersect(sK2,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_707,plain,
! [X0: $i] :
( intersect(X0,iPr_def_10)
| ~ intersect(X0,sK3) ),
inference(superposition,[status(thm)],[c_498,c_453]) ).
tcf(c_709,plain,
! [X0: $i] :
( intersect(X0,iPr_def_10)
| ~ intersect(X0,sK4) ),
inference(superposition,[status(thm)],[c_510,c_453]) ).
tcf(c_726,plain,
( intersect(sK2,iPr_def_10)
| ~ intersect(sK2,sK4) ),
inference(instantiation,[status(thm)],[c_709]) ).
tcf(c_728,plain,
( intersect(sK2,iPr_def_10)
| ~ intersect(sK2,sK3) ),
inference(instantiation,[status(thm)],[c_707]) ).
tcf(c_739,negated_conjecture,
~ intersect(sK2,sK4),
inference(global_subsumption_just,[status(thm)],[c_193,c_193,c_726]) ).
tcf(c_741,negated_conjecture,
~ intersect(sK2,sK3),
inference(global_subsumption_just,[status(thm)],[c_194,c_194,c_728]) ).
tcf(c_1207,plain,
! [X0: $i] :
( intersect(X0,sK4)
| member(sK0(iPr_def_10,X0),sK3)
| ~ intersect(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_559,c_454]) ).
tcf(c_1265,plain,
! [X0: $i] :
( intersect(X0,sK4)
| intersect(X0,sK3)
| ~ intersect(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_1207,c_454]) ).
tcf(c_1294,plain,
( intersect(sK2,sK4)
| intersect(sK2,sK3)
| ~ intersect(iPr_def_10,sK2) ),
inference(instantiation,[status(thm)],[c_1265]) ).
tcf(c_1295,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1294,c_741,c_739,c_693,c_192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET624+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 11:29:18 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 3.91/1.18 % SZS status Started for theBenchmark.p
% 3.91/1.18 % SZS status Theorem for theBenchmark.p
% 3.91/1.18
% 3.91/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.91/1.18
% 3.91/1.18 % ------ iProver source info
% 3.91/1.18
% 3.91/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 3.91/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.91/1.18 % git: non_committed_changes: false
% 3.91/1.18
% 3.91/1.18 % ------ Parsing...
% 3.91/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.91/1.18
% 3.91/1.18 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.91/1.18
% 3.91/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.91/1.18
% 3.91/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.91/1.18 % ------ Proving...
% 3.91/1.18 % ------ Problem Properties
% 3.91/1.18
% 3.91/1.18 %
% 3.91/1.18 % clauses 14
% 3.91/1.18 % conjectures 3
% 3.91/1.18 % EPR 5
% 3.91/1.18 % Horn 11
% 3.91/1.18 % unary 2
% 3.91/1.18 % binary 7
% 3.91/1.18 % lits 31
% 3.91/1.18 % lits eq 4
% 3.91/1.18 % fd_pure 0
% 3.91/1.18 % fd_pseudo 0
% 3.91/1.18 % fd_cond 0
% 3.91/1.18 % fd_pseudo_cond 2
% 3.91/1.18 % AC symbols 0
% 3.91/1.18
% 3.91/1.18 % ------ Schedule dynamic 5 is on
% 3.91/1.18
% 3.91/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.91/1.18
% 3.91/1.18
% 3.91/1.18 % ------
% 3.91/1.18 % Current options:
% 3.91/1.18 % ------
% 3.91/1.18
% 3.91/1.18
% 3.91/1.18 %
% 3.91/1.18
% 3.91/1.18 % ------ Proving...
% 3.91/1.18 %
% 3.91/1.18
% 3.91/1.18 % SZS status Theorem for theBenchmark.p
% 3.91/1.18
% 3.91/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.91/1.18
% 3.91/1.18
%------------------------------------------------------------------------------