%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET907+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 12:42:17 PM UTC 2026
% Result : Theorem 2.45s 1.10s
% Output : Refutation 2.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 9 unt; 0 def)
% Number of atoms : 50 ( 12 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 44 ( 16 ~; 11 |; 13 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% 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 : 35 ( 29 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f10,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f11,axiom,
! [X0,X1,X2] :
( subset(unordered_pair(X0,X1),X2)
<=> ( in(X0,X2)
& in(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(f12,conjecture,
! [X0,X1,X2] :
( ( in(X0,X1)
& in(X2,X1) )
=> set_union2(unordered_pair(X0,X2),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_zfmisc_1) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X2] :
( ( in(X0,X1)
& in(X2,X1) )
=> set_union2(unordered_pair(X0,X2),X1) = X1 ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f19,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f20,plain,
? [X0,X1,X2] :
( set_union2(unordered_pair(X0,X2),X1) != X1
& in(X0,X1)
& in(X2,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f21,plain,
? [X0,X1,X2] :
( set_union2(unordered_pair(X0,X2),X1) != X1
& in(X0,X1)
& in(X2,X1) ),
inference(flattening,[],[f20]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( subset(unordered_pair(X0,X1),X2)
| ~ in(X0,X2)
| ~ in(X1,X2) )
& ( ( in(X0,X2)
& in(X1,X2) )
| ~ subset(unordered_pair(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( subset(unordered_pair(X0,X1),X2)
| ~ in(X0,X2)
| ~ in(X1,X2) )
& ( ( in(X0,X2)
& in(X1,X2) )
| ~ subset(unordered_pair(X0,X1),X2) ) ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
( sK3 != set_union2(unordered_pair(sK2,sK4),sK3)
& in(sK2,sK3)
& in(sK4,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f21]) ).
fof(f28,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f36,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(cnf_transformation,[],[f19]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ in(X0,X2)
| subset(unordered_pair(X0,X1),X2)
| ~ in(X1,X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f40,plain,
in(sK4,sK3),
inference(cnf_transformation,[],[f26]) ).
fof(f41,plain,
in(sK2,sK3),
inference(cnf_transformation,[],[f26]) ).
fof(f42,plain,
sK3 != set_union2(unordered_pair(sK2,sK4),sK3),
inference(cnf_transformation,[],[f26]) ).
fof(f62,plain,
! [X0] :
( ~ in(X0,sK3)
| subset(unordered_pair(sK4,X0),sK3) ),
inference(resolution,[],[f39,f40]) ).
fof(f66,plain,
subset(unordered_pair(sK4,sK2),sK3),
inference(resolution,[],[f62,f41]) ).
fof(f67,plain,
subset(unordered_pair(sK2,sK4),sK3),
inference(forward_demodulation,[],[f66,f28]) ).
fof(f76,plain,
sK3 = set_union2(unordered_pair(sK2,sK4),sK3),
inference(resolution,[],[f67,f36]) ).
fof(f77,plain,
$false,
inference(forward_subsumption_resolution,[],[f76,f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET907+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n008.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 03:09:55 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.45/1.10 % (1831661)Detected formulas, will run a generic FOF schedule.
% 2.45/1.10 % (1831671)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3412326466:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.45/1.10 % (1831671)First to succeed.
% 2.45/1.10 % (1831671)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1831661"
% 2.45/1.10 % (1831666)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=1739977995:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.45/1.10 % (1831670)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1533773406:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.45/1.10 % (1831668)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=2572666273:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.45/1.10 % (1831672)dis-21_1_sil=8000:lcm=predicate:random_seed=35418036: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)
% 2.45/1.10 % (1831669)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3594447512:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.45/1.10 % (1831667)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=2600544662:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.45/1.10 % (1831669)Refutation not found, incomplete strategy
% 2.45/1.10 % (1831669)------------------------------
% 2.45/1.10 % (1831669)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.45/1.10 % (1831669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.45/1.10 % (1831669)CaDiCaL version: 2.1.3
% 2.45/1.10 % (1831669)Termination reason: Refutation not found, incomplete strategy
% 2.45/1.10 % (1831669)Time elapsed: 0.001 s
% 2.45/1.10 % (1831669)Peak memory usage: 88 MB
% 2.45/1.10 % (1831672)Also succeeded, but the first one will report.
% 2.45/1.10 % (1831670)Also succeeded, but the first one will report.
% 2.45/1.10 % (1831671)Refutation found. Thanks to Tanya!
% 2.45/1.10 % SZS status Theorem for theBenchmark
% 2.45/1.10 % SZS output start Proof for theBenchmark
% See solution above
% 2.45/1.10 % (1831671)------------------------------
% 2.45/1.10 % (1831671)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.45/1.10 % (1831671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.45/1.10 % (1831671)CaDiCaL version: 2.1.3
% 2.45/1.10 % (1831671)Termination reason: Refutation
% 2.45/1.10 % (1831671)Time elapsed: 0.002 s
% 2.45/1.10 % (1831671)Peak memory usage: 89 MB
% 2.45/1.10 % (1831671)Instructions burned: 3 (million)
% 2.45/1.10 % (1831671)------------------------------
% 2.45/1.10 % (1831671)------------------------------
% 2.45/1.10 % (1831661)Success in time 0.296 s
% 2.45/1.10 % Vampire exiting
%------------------------------------------------------------------------------