%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET630+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 : n016.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 02:47:37 PM UTC 2026
% Result : Theorem 3.39s 6.28s
% Output : CNFRefutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 44 ( 28 unt; 4 def)
% Number of atoms : 102 ( 9 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 63 ( 32 ~; 24 |; 5 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 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 : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn 55 !; 2 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_defn) ).
fof(f2,axiom,
! [X0,X1,X2] :
( intersect(X0,union(X1,X2))
<=> ( intersect(X0,X2)
| intersect(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_with_union) ).
fof(f3,axiom,
! [X0,X1] : disjoint(intersection(X0,X1),difference(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_and_union_disjoint) ).
fof(f6,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> ~ intersect(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint_defn) ).
fof(f8,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f12,conjecture,
! [X0,X1] : disjoint(intersection(X0,X1),symmetric_difference(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_intersection_and_symmetric_difference_disjoint) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] : disjoint(intersection(X0,X1),symmetric_difference(X0,X1)),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f15,plain,
? [X0,X1] : ~ disjoint(intersection(X0,X1),symmetric_difference(X0,X1)),
inference(ennf_transformation,[],[f13]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ( ~ intersect(X0,union(X1,X2))
| intersect(X0,X2)
| intersect(X0,X1) )
& ( ( ~ intersect(X0,X2)
& ~ intersect(X0,X1) )
| intersect(X0,union(X1,X2)) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ( ~ intersect(X0,union(X1,X2))
| intersect(X0,X2)
| intersect(X0,X1) )
& ( ( ~ intersect(X0,X2)
& ~ intersect(X0,X1) )
| intersect(X0,union(X1,X2)) ) ),
inference(flattening,[],[f16]) ).
fof(f23,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ~ intersect(X0,X1) )
& ( intersect(X0,X1)
| disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f27,plain,
~ disjoint(intersection(sK2,sK3),symmetric_difference(sK2,sK3)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f15]) ).
fof(f28,plain,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[],[f1]) ).
fof(f29,plain,
! [X2,X0,X1] :
( ~ intersect(X0,union(X1,X2))
| intersect(X0,X2)
| intersect(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f32,plain,
! [X0,X1] : disjoint(intersection(X0,X1),difference(X0,X1)),
inference(cnf_transformation,[],[f3]) ).
fof(f39,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f40,plain,
! [X0,X1] :
( intersect(X0,X1)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f42,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f8]) ).
fof(f49,plain,
~ disjoint(intersection(sK2,sK3),symmetric_difference(sK2,sK3)),
inference(cnf_transformation,[],[f27]) ).
fof(f51,plain,
~ disjoint(intersection(sK2,sK3),union(difference(sK2,sK3),difference(sK3,sK2))),
inference(definition_unfolding,[],[f49,f28]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( intersect(X0,X2)
| intersect(X0,X1)
| ~ intersect(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] : disjoint(intersection(X0,X1),difference(X0,X1)),
inference(cnf_transformation,[],[f32]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| intersect(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ~ disjoint(X0,X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f42]) ).
tcf(c_67,negated_conjecture,
~ disjoint(intersection(sK2,sK3),union(difference(sK2,sK3),difference(sK3,sK2))),
inference(cnf_transformation,[],[f51]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] :
( ~ intersect(X0,X1)
| ~ disjoint(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_60]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( ~ disjoint(X0,X1)
| ~ intersect(X0,X1) ),
inference(renaming,[status(thm)],[c_82]) ).
tcf(c_145,plain,
! [X0: $i,X1: $i,X2: $i] :
( intersect(X0,X2)
| ~ disjoint(X0,X1)
| ~ intersect(X0,union(X1,X2)) ),
inference(bin_hyper_res,[status(thm)],[c_51,c_83]) ).
tcf(c_504,definition,
iPr_def_10 = intersection(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_505,definition,
iPr_def_11 = difference(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_506,definition,
iPr_def_12 = difference(sK3,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_507,definition,
iPr_def_13 = union(iPr_def_11,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_508,negated_conjecture,
~ disjoint(iPr_def_10,iPr_def_13),
inference(demodulation,[status(thm)],[c_67,c_506,c_505,c_507,c_504]) ).
tcf(c_940,plain,
intersect(iPr_def_10,iPr_def_13),
inference(superposition,[status(thm)],[c_59,c_508]) ).
tcf(c_942,plain,
disjoint(intersection(sK2,sK3),iPr_def_11),
inference(superposition,[status(thm)],[c_505,c_52]) ).
tcf(c_943,plain,
disjoint(intersection(sK3,sK2),iPr_def_12),
inference(superposition,[status(thm)],[c_506,c_52]) ).
tcf(c_944,plain,
disjoint(iPr_def_10,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_942,c_504]) ).
tcf(c_978,plain,
disjoint(iPr_def_10,iPr_def_12),
inference(demodulation,[status(thm)],[c_943,c_62,c_504]) ).
tcf(c_2281,plain,
! [X0: $i] :
( intersect(X0,iPr_def_12)
| ~ disjoint(X0,iPr_def_11)
| ~ intersect(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_507,c_145]) ).
tcf(c_2376,plain,
( intersect(iPr_def_10,iPr_def_12)
| ~ disjoint(iPr_def_10,iPr_def_11) ),
inference(superposition,[status(thm)],[c_940,c_2281]) ).
tcf(c_2388,plain,
intersect(iPr_def_10,iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_2376,c_944]) ).
tcf(c_2520,plain,
~ disjoint(iPr_def_10,iPr_def_12),
inference(superposition,[status(thm)],[c_2388,c_60]) ).
tcf(c_2521,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2520,c_978]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET630+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/5.37 % Computer : n016.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Thu Sep 24 11:35:35 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/5.41 Running first-order theorem proving
% 0.15/5.41 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
% 0.15/5.42
% 0.15/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.42
% 0.15/5.42 % Detected problem language: tptp
% 0.15/5.43 % Proving...
% 3.39/6.28 % SZS status Started for theBenchmark.p
% 3.39/6.28 % SZS status Theorem for theBenchmark.p
% 3.39/6.28
% 3.39/6.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.39/6.28
% 3.39/6.28 % ------ iProver source info
% 3.39/6.28
% 3.39/6.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.39/6.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.39/6.28 % git: non_committed_changes: false
% 3.39/6.28
% 3.39/6.28 % ------ Parsing...
% 3.39/6.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.39/6.28
% 3.39/6.28 % ------ 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 %
% 3.39/6.28
% 3.39/6.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.39/6.28
% 3.39/6.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.39/6.28 % ------ Proving...
% 3.39/6.28 % ------ Problem Properties
% 3.39/6.28
% 3.39/6.28 %
% 3.39/6.28 % clauses 22
% 3.39/6.28 % conjectures 1
% 3.39/6.28 % EPR 5
% 3.39/6.28 % Horn 16
% 3.39/6.28 % unary 8
% 3.39/6.28 % binary 9
% 3.39/6.28 % lits 41
% 3.39/6.28 % lits eq 8
% 3.39/6.28 % fd_pure 0
% 3.39/6.28 % fd_pseudo 0
% 3.39/6.28 % fd_cond 0
% 3.39/6.28 % fd_pseudo_cond 2
% 3.39/6.28 % AC symbols 0
% 3.39/6.28
% 3.39/6.28 % ------ Schedule dynamic 5 is on
% 3.39/6.28
% 3.39/6.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.39/6.28
% 3.39/6.28
% 3.39/6.28 % ------
% 3.39/6.28 % Current options:
% 3.39/6.28 % ------
% 3.39/6.28
% 3.39/6.28
% 3.39/6.28 %
% 3.39/6.28
% 3.39/6.28 % ------ Proving...
% 3.39/6.28 %
% 3.39/6.28
% 3.39/6.28 % SZS status Theorem for theBenchmark.p
% 3.39/6.28
% 3.39/6.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.39/6.28
% 3.39/6.28
%------------------------------------------------------------------------------