TSTP Solution File: SET635+3 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET635+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 15:08:59 EDT 2024
% Result : Theorem 0.23s 0.41s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 27 unt; 0 def)
% Number of atoms : 37 ( 30 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 18 ( 12 ~; 3 |; 1 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% 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 : 54 ( 48 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1062,plain,
$false,
inference(trivial_inequality_removal,[],[f1061]) ).
fof(f1061,plain,
intersection(sK0,difference(sK1,sK2)) != intersection(sK0,difference(sK1,sK2)),
inference(superposition,[],[f1034,f738]) ).
fof(f738,plain,
! [X2,X0,X1] : intersection(X0,difference(X1,X2)) = intersection(X1,difference(X0,X2)),
inference(superposition,[],[f162,f56]) ).
fof(f56,plain,
! [X2,X0,X1] : intersection(X0,difference(X1,X2)) = difference(intersection(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
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(f162,plain,
! [X2,X0,X1] : intersection(X0,difference(X1,X2)) = difference(intersection(X1,X0),X2),
inference(superposition,[],[f56,f43]) ).
fof(f43,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f1034,plain,
intersection(sK0,difference(sK1,sK2)) != intersection(sK1,difference(sK0,sK2)),
inference(backward_demodulation,[],[f742,f1029]) ).
fof(f1029,plain,
! [X0,X1] : difference(X0,X1) = difference(X0,intersection(X0,X1)),
inference(forward_demodulation,[],[f1013,f68]) ).
fof(f68,plain,
! [X0] : union(empty_set,X0) = X0,
inference(superposition,[],[f42,f40]) ).
fof(f40,plain,
! [X0] : union(X0,empty_set) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : union(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_empty_set) ).
fof(f42,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f1013,plain,
! [X0,X1] : difference(X0,intersection(X0,X1)) = union(empty_set,difference(X0,X1)),
inference(superposition,[],[f57,f81]) ).
fof(f81,plain,
! [X0] : empty_set = difference(X0,X0),
inference(resolution,[],[f55,f39]) ).
fof(f39,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
fof(f55,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| difference(X0,X1) = empty_set ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1] :
( ( difference(X0,X1) = empty_set
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| difference(X0,X1) != empty_set ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_empty_set) ).
fof(f57,plain,
! [X2,X0,X1] : difference(X0,intersection(X1,X2)) = union(difference(X0,X1),difference(X0,X2)),
inference(cnf_transformation,[],[f4]) ).
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(f742,plain,
intersection(sK0,difference(sK1,sK2)) != intersection(sK1,difference(sK0,intersection(sK0,sK2))),
inference(superposition,[],[f37,f162]) ).
fof(f37,plain,
intersection(sK0,difference(sK1,sK2)) != difference(intersection(sK0,sK1),intersection(sK0,sK2)),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
intersection(sK0,difference(sK1,sK2)) != difference(intersection(sK0,sK1),intersection(sK0,sK2)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f18,f20]) ).
fof(f20,plain,
( ? [X0,X1,X2] : intersection(X0,difference(X1,X2)) != difference(intersection(X0,X1),intersection(X0,X2))
=> intersection(sK0,difference(sK1,sK2)) != difference(intersection(sK0,sK1),intersection(sK0,sK2)) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
? [X0,X1,X2] : intersection(X0,difference(X1,X2)) != difference(intersection(X0,X1),intersection(X0,X2)),
inference(ennf_transformation,[],[f17]) ).
fof(f17,negated_conjecture,
~ ! [X0,X1,X2] : intersection(X0,difference(X1,X2)) = difference(intersection(X0,X1),intersection(X0,X2)),
inference(negated_conjecture,[],[f16]) ).
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) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET635+3 : TPTP v8.1.2. Released v2.2.0.
% 0.08/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n004.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Apr 30 01:17:03 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (27459)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (27462)WARNING: value z3 for option sas not known
% 0.15/0.38 % (27461)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (27460)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (27463)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (27462)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38 % (27464)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.38 % (27465)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.38 % (27466)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.39 TRYING [3]
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 TRYING [4]
% 0.15/0.40 TRYING [1]
% 0.15/0.40 TRYING [2]
% 0.15/0.40 TRYING [3]
% 0.15/0.40 TRYING [3]
% 0.23/0.41 % (27465)First to succeed.
% 0.23/0.41 TRYING [4]
% 0.23/0.41 % (27465)Refutation found. Thanks to Tanya!
% 0.23/0.41 % SZS status Theorem for theBenchmark
% 0.23/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.41 % (27465)------------------------------
% 0.23/0.41 % (27465)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.23/0.41 % (27465)Termination reason: Refutation
% 0.23/0.41
% 0.23/0.41 % (27465)Memory used [KB]: 1112
% 0.23/0.41 % (27465)Time elapsed: 0.031 s
% 0.23/0.41 % (27465)Instructions burned: 49 (million)
% 0.23/0.41 % (27465)------------------------------
% 0.23/0.41 % (27465)------------------------------
% 0.23/0.41 % (27459)Success in time 0.048 s
%------------------------------------------------------------------------------