%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET635+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 : n002.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 02:47:39 PM UTC 2026
% Result : Theorem 4.74s 16.32s
% Output : CNFRefutation 4.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 28 unt; 0 def)
% Number of atoms : 38 ( 29 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 18 ( 12 ~; 4 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn 55 !; 3 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : subset(intersection(X0,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_is_subset) ).
fof(f2,axiom,
! [X0,X1] :
( difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_empty_set) ).
fof(f3,axiom,
! [X0] : union(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_empty_set) ).
fof(f4,axiom,
! [X0,X1,X2] : difference(X0,intersection(X1,X2)) = union(difference(X0,X1),difference(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_and_intersection_and_union) ).
fof(f5,axiom,
! [X0,X1,X2] : intersection(X0,difference(X1,X2)) = difference(intersection(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_and_intersection) ).
fof(f11,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f16,conjecture,
! [X0,X1,X2] : intersection(X0,difference(X1,X2)) = difference(intersection(X0,X1),intersection(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th117) ).
fof(f17,negated_conjecture,
~ ! [X0,X1,X2] : intersection(X0,difference(X1,X2)) = difference(intersection(X0,X1),intersection(X0,X2)),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f19,plain,
? [X0,X1,X2] : intersection(X0,difference(X1,X2)) != difference(intersection(X0,X1),intersection(X0,X2)),
inference(ennf_transformation,[],[f17]) ).
fof(f20,plain,
! [X0,X1] :
( ( difference(X0,X1) != empty_set
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| difference(X0,X1) = empty_set ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f33,plain,
intersection(sK2,difference(sK3,sK4)) != difference(intersection(sK2,sK3),intersection(sK2,sK4)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f19]) ).
fof(f34,plain,
! [X0,X1] : subset(intersection(X0,X1),X0),
inference(cnf_transformation,[],[f1]) ).
fof(f36,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| difference(X0,X1) = empty_set ),
inference(cnf_transformation,[],[f20]) ).
fof(f37,plain,
! [X0] : union(X0,empty_set) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f38,plain,
! [X2,X0,X1] : difference(X0,intersection(X1,X2)) = union(difference(X0,X1),difference(X0,X2)),
inference(cnf_transformation,[],[f4]) ).
fof(f39,plain,
! [X2,X0,X1] : intersection(X0,difference(X1,X2)) = difference(intersection(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f51,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f60,plain,
intersection(sK2,difference(sK3,sK4)) != difference(intersection(sK2,sK3),intersection(sK2,sK4)),
inference(cnf_transformation,[],[f33]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : subset(intersection(X0,X1),X0),
inference(cnf_transformation,[],[f34]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( ( difference(X0,X1) = empty_set )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_52,plain,
! [X0: $i] : union(X0,empty_set) = X0,
inference(cnf_transformation,[],[f37]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] : union(difference(X0,X1),difference(X0,X2)) = difference(X0,intersection(X1,X2)),
inference(cnf_transformation,[],[f38]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(X0,difference(X1,X2)) = difference(intersection(X0,X1),X2),
inference(cnf_transformation,[],[f39]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f51]) ).
tcf(c_73,negated_conjecture,
difference(intersection(sK2,sK3),intersection(sK2,sK4)) != intersection(sK2,difference(sK3,sK4)),
inference(cnf_transformation,[],[f60]) ).
tcf(c_233,plain,
difference(intersection(sK2,sK3),intersection(sK4,sK2)) != intersection(sK2,difference(sK3,sK4)),
inference(demodulation,[status(thm)],[c_73,c_66]) ).
tcf(c_234,plain,
difference(intersection(sK2,sK3),intersection(sK4,sK2)) != difference(intersection(sK2,sK3),sK4),
inference(demodulation,[status(thm)],[c_233,c_54]) ).
tcf(c_284,plain,
! [X0: $i,X1: $i] : difference(intersection(X0,X1),X0) = empty_set,
inference(superposition,[status(thm)],[c_49,c_50]) ).
tcf(c_803,plain,
! [X0: $i,X1: $i,X2: $i] : difference(intersection(X0,X1),intersection(X2,X0)) = union(difference(intersection(X0,X1),X2),empty_set),
inference(superposition,[status(thm)],[c_284,c_53]) ).
tcf(c_815,plain,
! [X0: $i,X1: $i,X2: $i] : difference(intersection(X0,X1),intersection(X2,X0)) = difference(intersection(X0,X1),X2),
inference(demodulation,[status(thm)],[c_803,c_52]) ).
tcf(c_8467,plain,
difference(intersection(sK2,sK3),sK4) != difference(intersection(sK2,sK3),sK4),
inference(demodulation,[status(thm)],[c_234,c_815]) ).
tcf(c_8468,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_8467]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET635+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/15.39 % Computer : n002.cluster.edu
% 0.10/15.39 % Model : x86_64 x86_64
% 0.10/15.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/15.39 % Memory : 8046.5625MB
% 0.10/15.39 % OS : Linux 6.8.0-71-generic
% 0.10/15.39 % CPULimit : 300
% 0.10/15.39 % WCLimit : 300
% 0.10/15.39 % DateTime : Thu Sep 24 11:34:38 UTC 2026
% 0.10/15.39 % CPUTime :
% 0.10/15.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/15.43 Running first-order theorem proving
% 0.15/15.43 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
% 0.15/15.44
% 0.15/15.44 % ======== iProver multi-core TPTP/SMT =========
% 0.15/15.44
% 0.15/15.44 % Detected problem language: tptp
% 0.15/15.45 % Proving...
% 4.74/16.32 % SZS status Started for theBenchmark.p
% 4.74/16.32 % SZS status Theorem for theBenchmark.p
% 4.74/16.32
% 4.74/16.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.74/16.32
% 4.74/16.32 % ------ iProver source info
% 4.74/16.32
% 4.74/16.32 % git: date: 2026-07-19 20:42:38 +0200
% 4.74/16.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.74/16.32 % git: non_committed_changes: false
% 4.74/16.32
% 4.74/16.32 % ------ Parsing...
% 4.74/16.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.74/16.32
% 4.74/16.32 % ------ Preprocessing... sup_sim: 0 pe_s pe_e sup_sim: 0 pe_s pe_e %
% 4.74/16.32
% 4.74/16.32 % ------ Preprocessing... gs_s sp: 0 0s gs_e scvd_s sp: 0 0s scvd_e snvd_s sp: 0 0s snvd_e %
% 4.74/16.32
% 4.74/16.32 % ------ Preprocessing...
% 4.74/16.32 % ------ Proving...
% 4.74/16.32 % ------ Problem Properties
% 4.74/16.32
% 4.74/16.32 %
% 4.74/16.32 % clauses 24
% 4.74/16.32 % conjectures 1
% 4.74/16.32 % EPR 4
% 4.74/16.32 % Horn 21
% 4.74/16.32 % unary 9
% 4.74/16.32 % binary 9
% 4.74/16.32 % lits 45
% 4.74/16.32 % lits eq 11
% 4.74/16.32 % fd_pure 0
% 4.74/16.32 % fd_pseudo 0
% 4.74/16.32 % fd_cond 0
% 4.74/16.32 % fd_pseudo_cond 3
% 4.74/16.32 % AC symbols 0
% 4.74/16.32
% 4.74/16.32 % ------ Input Options Time Limit: Unbounded
% 4.74/16.32
% 4.74/16.32
% 4.74/16.32 % ------
% 4.74/16.32 % Current options:
% 4.74/16.32 % ------
% 4.74/16.32
% 4.74/16.32
% 4.74/16.32 %
% 4.74/16.32
% 4.74/16.32 % ------ Proving...
% 4.74/16.32 %
% 4.74/16.32
% 4.74/16.32 % SZS status Theorem for theBenchmark.p
% 4.74/16.32
% 4.74/16.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.74/16.33
% 4.74/16.33
%------------------------------------------------------------------------------