%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET928+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 : Tue Sep 29 12:42:21 PM UTC 2026
% Result : Theorem 3.56s 1.39s
% Output : Refutation 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 7 unt; 0 def)
% Number of atoms : 92 ( 22 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 102 ( 46 ~; 39 |; 13 &)
% ( 3 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 48 ( 39 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f6,axiom,
! [X0,X1,X2] :
~ ( disjoint(unordered_pair(X0,X1),X2)
& in(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_zfmisc_1) ).
fof(f7,axiom,
! [X0,X1,X2] :
~ ( ~ in(X0,X1)
& ~ in(X2,X1)
& ~ disjoint(unordered_pair(X0,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_zfmisc_1) ).
fof(f8,conjecture,
! [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = unordered_pair(X0,X1)
<=> ( ~ in(X0,X2)
& ~ in(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = unordered_pair(X0,X1)
<=> ( ~ in(X0,X2)
& ~ in(X1,X2) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_difference(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(f11,plain,
? [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = unordered_pair(X0,X1)
<~> ( ~ in(X0,X2)
& ~ in(X1,X2) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f12,plain,
! [X0,X1,X2] :
( in(X0,X1)
| in(X2,X1)
| disjoint(unordered_pair(X0,X2),X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ~ disjoint(unordered_pair(X0,X1),X2)
| ~ in(X0,X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f16,plain,
? [X0,X1,X2] :
( ( in(X0,X2)
| in(X1,X2)
| unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2) )
& ( ( ~ in(X0,X2)
& ~ in(X1,X2) )
| set_difference(unordered_pair(X0,X1),X2) = unordered_pair(X0,X1) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f17,plain,
? [X0,X1,X2] :
( ( in(X0,X2)
| in(X1,X2)
| unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2) )
& ( ( ~ in(X0,X2)
& ~ in(X1,X2) )
| set_difference(unordered_pair(X0,X1),X2) = unordered_pair(X0,X1) ) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
( ( in(sK0,sK2)
| in(sK1,sK2)
| unordered_pair(sK0,sK1) != set_difference(unordered_pair(sK0,sK1),sK2) )
& ( ( ~ in(sK0,sK2)
& ~ in(sK1,sK2) )
| unordered_pair(sK0,sK1) = set_difference(unordered_pair(sK0,sK1),sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_difference(X0,X1) != X0 )
& ( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f20,plain,
( unordered_pair(sK0,sK1) = set_difference(unordered_pair(sK0,sK1),sK2)
| ~ in(sK1,sK2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f21,plain,
( unordered_pair(sK0,sK1) = set_difference(unordered_pair(sK0,sK1),sK2)
| ~ in(sK0,sK2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f22,plain,
( unordered_pair(sK0,sK1) != set_difference(unordered_pair(sK0,sK1),sK2)
| in(sK1,sK2)
| in(sK0,sK2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f23,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f24,plain,
! [X2,X0,X1] :
( disjoint(unordered_pair(X0,X2),X1)
| in(X2,X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f25,plain,
! [X2,X0,X1] :
( ~ disjoint(unordered_pair(X0,X1),X2)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f13]) ).
fof(f27,plain,
! [X0,X1] :
( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f28,plain,
! [X0,X1] :
( set_difference(X0,X1) != X0
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ disjoint(unordered_pair(X0,X1),X2)
| ~ in(X1,X2) ),
inference(superposition,[],[f25,f23]) ).
fof(f36,plain,
( unordered_pair(sK0,sK1) != unordered_pair(sK0,sK1)
| in(sK1,sK2)
| in(sK0,sK2)
| ~ disjoint(unordered_pair(sK0,sK1),sK2) ),
inference(superposition,[],[f22,f27]) ).
fof(f37,plain,
( in(sK1,sK2)
| in(sK0,sK2)
| ~ disjoint(unordered_pair(sK0,sK1),sK2) ),
inference(trivial_inequality_removal,[],[f36]) ).
fof(f38,plain,
( ~ disjoint(unordered_pair(sK0,sK1),sK2)
| in(sK1,sK2) ),
inference(forward_subsumption_resolution,[],[f37,f25]) ).
fof(f41,plain,
( unordered_pair(sK0,sK1) != unordered_pair(sK0,sK1)
| disjoint(unordered_pair(sK0,sK1),sK2)
| ~ in(sK0,sK2) ),
inference(superposition,[],[f28,f21]) ).
fof(f42,plain,
( unordered_pair(sK0,sK1) != unordered_pair(sK0,sK1)
| disjoint(unordered_pair(sK0,sK1),sK2)
| ~ in(sK1,sK2) ),
inference(superposition,[],[f28,f20]) ).
fof(f44,plain,
( disjoint(unordered_pair(sK0,sK1),sK2)
| ~ in(sK1,sK2) ),
inference(trivial_inequality_removal,[],[f42]) ).
fof(f45,plain,
( disjoint(unordered_pair(sK0,sK1),sK2)
| ~ in(sK0,sK2) ),
inference(trivial_inequality_removal,[],[f41]) ).
fof(f46,plain,
~ in(sK0,sK2),
inference(forward_subsumption_resolution,[],[f45,f25]) ).
fof(f48,plain,
( in(sK1,sK2)
| in(sK0,sK2)
| in(sK1,sK2) ),
inference(resolution,[],[f24,f38]) ).
fof(f51,plain,
( in(sK1,sK2)
| in(sK0,sK2) ),
inference(duplicate_literal_removal,[],[f48]) ).
fof(f52,plain,
in(sK1,sK2),
inference(forward_subsumption_resolution,[],[f51,f46]) ).
fof(f54,plain,
disjoint(unordered_pair(sK0,sK1),sK2),
inference(forward_subsumption_resolution,[],[f44,f52]) ).
fof(f62,plain,
~ in(sK1,sK2),
inference(resolution,[],[f34,f54]) ).
fof(f66,plain,
$false,
inference(forward_subsumption_resolution,[],[f62,f52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET928+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n018.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 03:17:52 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.56/1.39 % (2963178)Detected formulas, will run a generic FOF schedule.
% 3.56/1.39 % (2963246)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3552938396:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.56/1.39 % (2963244)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2520734222:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.56/1.39 % (2963245)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=32345534:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.56/1.39 % (2963249)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=790546867:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.56/1.39 % (2963247)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2939998892:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.56/1.39 % (2963250)dis-21_1_sil=8000:lcm=predicate:random_seed=921220301:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.56/1.39 % (2963248)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=470340352:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.56/1.39 % (2963247)Refutation not found, incomplete strategy
% 3.56/1.39 % (2963247)------------------------------
% 3.56/1.39 % (2963247)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.39 % (2963247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.39 % (2963247)CaDiCaL version: 2.1.3
% 3.56/1.39 % (2963247)Termination reason: Refutation not found, incomplete strategy
% 3.56/1.39 % (2963247)Time elapsed: 0.002 s
% 3.56/1.39 % (2963247)Peak memory usage: 88 MB
% 3.56/1.39 % (2963247)Instructions burned: 1 (million)
% 3.56/1.39 % (2963248)First to succeed.
% 3.56/1.39 % (2963249)Also succeeded, but the first one will report.
% 3.56/1.39 % (2963248)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2963178"
% 3.56/1.39 % (2963250)Instruction limit reached!
% 3.56/1.39 % (2963250)------------------------------
% 3.56/1.39 % (2963250)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.39 % (2963250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.39 % (2963250)CaDiCaL version: 2.1.3
% 3.56/1.39 % (2963250)Termination reason: Instruction limit
% 3.56/1.39 % (2963250)Termination phase: Saturation
% 3.56/1.39 % (2963250)Time elapsed: 0.070 s
% 3.56/1.39 % (2963250)Peak memory usage: 88 MB
% 3.56/1.39 % (2963250)Instructions burned: 130 (million)
% 3.56/1.39 % (2963258)lrs+10_1_sil=8000:sp=occurrence:random_seed=3741180318:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.56/1.39 % (2963258)Also succeeded, but the first one will report.
% 3.56/1.39 % (2963247)------------------------------
% 3.56/1.39 % (2963247)------------------------------
% 3.56/1.39 % (2963248)Refutation found. Thanks to Tanya!
% 3.56/1.39 % SZS status Theorem for theBenchmark
% 3.56/1.39 % SZS output start Proof for theBenchmark
% See solution above
% 3.56/1.39 % (2963248)------------------------------
% 3.56/1.39 % (2963248)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.39 % (2963248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.39 % (2963248)CaDiCaL version: 2.1.3
% 3.56/1.39 % (2963248)Termination reason: Refutation
% 3.56/1.39 % (2963248)Time elapsed: 0.003 s
% 3.56/1.39 % (2963248)Peak memory usage: 88 MB
% 3.56/1.39 % (2963248)Instructions burned: 3 (million)
% 3.56/1.39 % (2963248)------------------------------
% 3.56/1.39 % (2963248)------------------------------
% 3.56/1.39 % (2963178)Success in time 0.431 s
% 3.56/1.39 % Vampire exiting
%------------------------------------------------------------------------------