%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET958+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 : n011.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 12:42:25 PM UTC 2026
% Result : Theorem 2.73s 1.35s
% Output : Refutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 22 ( 3 unt; 0 def)
% Number of atoms : 74 ( 7 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 86 ( 34 ~; 25 |; 18 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 65 ( 55 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f9,conjecture,
! [X0,X1] :
( ( ! [X2] :
~ ( in(X2,X0)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) )
& ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
=> in(ordered_pair(X2,X3),X1) ) )
=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t111_zfmisc_1) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] :
( ( ! [X2] :
~ ( in(X2,X0)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) )
& ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
=> in(ordered_pair(X2,X3),X1) ) )
=> subset(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
~ ! [X0,X1] :
( ( ! [X2] :
~ ( in(X2,X0)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) )
& ! [X5,X6] :
( in(ordered_pair(X5,X6),X0)
=> in(ordered_pair(X5,X6),X1) ) )
=> subset(X0,X1) ),
inference(rectify,[],[f10]) ).
fof(f14,plain,
? [X0,X1] :
( ~ subset(X0,X1)
& ! [X2] :
( ~ in(X2,X0)
| ? [X3,X4] : ordered_pair(X3,X4) = X2 )
& ! [X5,X6] :
( in(ordered_pair(X5,X6),X1)
| ~ in(ordered_pair(X5,X6),X0) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f15,plain,
? [X0,X1] :
( ~ subset(X0,X1)
& ! [X2] :
( ~ in(X2,X0)
| ? [X3,X4] : ordered_pair(X3,X4) = X2 )
& ! [X5,X6] :
( in(ordered_pair(X5,X6),X1)
| ~ in(ordered_pair(X5,X6),X0) ) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f18,plain,
( ~ subset(sK0,sK1)
& ! [X2] :
( ~ in(X2,sK0)
| ordered_pair(sK2(X2),sK3(X2)) = X2 )
& ! [X5,X6] :
( in(ordered_pair(X5,X6),sK1)
| ~ in(ordered_pair(X5,X6),sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X3,sK2(X2)),skolemize(X4,sK3(X2))],[f15]) ).
fof(f19,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f20,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK4(X0,X1),X1)
& in(sK4(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f20]) ).
fof(f22,plain,
! [X6,X5] :
( ~ in(ordered_pair(X5,X6),sK0)
| in(ordered_pair(X5,X6),sK1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f23,plain,
! [X2] :
( ordered_pair(sK2(X2),sK3(X2)) = X2
| ~ in(X2,sK0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f24,plain,
~ subset(sK0,sK1),
inference(cnf_transformation,[],[f18]) ).
fof(f26,plain,
! [X0,X1] :
( in(sK4(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f27,plain,
! [X0,X1] :
( ~ in(sK4(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f30,plain,
! [X0] :
( ~ in(X0,sK0)
| in(X0,sK1)
| ~ in(X0,sK0) ),
inference(superposition,[],[f22,f23]) ).
fof(f31,plain,
! [X0] :
( ~ in(X0,sK0)
| in(X0,sK1) ),
inference(duplicate_literal_removal,[],[f30]) ).
fof(f32,plain,
! [X0] :
( in(sK4(sK0,X0),sK1)
| subset(sK0,X0) ),
inference(resolution,[],[f31,f26]) ).
fof(f33,plain,
( subset(sK0,sK1)
| subset(sK0,sK1) ),
inference(resolution,[],[f32,f27]) ).
fof(f35,plain,
subset(sK0,sK1),
inference(duplicate_literal_removal,[],[f33]) ).
fof(f36,plain,
$false,
inference(forward_subsumption_resolution,[],[f35,f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET958+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n011.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 03:16:30 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 Running first-order theorem proving
% 0.16/0.42 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
% 2.73/1.35 % (2984503)Detected formulas, will run a generic FOF schedule.
% 2.73/1.35 % (2984511)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2882248118:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.73/1.35 % (2984511)First to succeed.
% 2.73/1.35 % (2984511)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2984503"
% 2.73/1.35 % (2984514)dis-21_1_sil=8000:lcm=predicate:random_seed=2659783907: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)
% 2.73/1.35 % (2984510)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=4101880983:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.73/1.35 % (2984509)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=4135531497:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.73/1.35 % (2984508)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=1216385181:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.73/1.35 % (2984512)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3647065340:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.73/1.35 % (2984512)Also succeeded, but the first one will report.
% 2.73/1.35 % (2984513)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4174847601:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.73/1.35 % (2984513)Also succeeded, but the first one will report.
% 2.73/1.35 % (2984514)Instruction limit reached!
% 2.73/1.35 % (2984514)------------------------------
% 2.73/1.35 % (2984514)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.35 % (2984514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.35 % (2984514)CaDiCaL version: 2.1.3
% 2.73/1.35 % (2984514)Termination reason: Instruction limit
% 2.73/1.35 % (2984514)Termination phase: Saturation
% 2.73/1.35 % (2984514)Time elapsed: 0.072 s
% 2.73/1.35 % (2984514)Peak memory usage: 88 MB
% 2.73/1.35 % (2984514)Instructions burned: 130 (million)
% 2.73/1.35 % (2984511)Refutation found. Thanks to Tanya!
% 2.73/1.35 % SZS status Theorem for theBenchmark
% 2.73/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.73/1.35 % (2984511)------------------------------
% 2.73/1.35 % (2984511)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.35 % (2984511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.35 % (2984511)CaDiCaL version: 2.1.3
% 2.73/1.35 % (2984511)Termination reason: Refutation
% 2.73/1.35 % (2984511)Time elapsed: 0.001 s
% 2.73/1.35 % (2984511)Peak memory usage: 88 MB
% 2.73/1.35 % (2984511)Instructions burned: 1 (million)
% 2.73/1.35 % (2984511)------------------------------
% 2.73/1.35 % (2984511)------------------------------
% 2.73/1.35 % (2984503)Success in time 0.301 s
% 2.73/1.35 % Vampire exiting
%------------------------------------------------------------------------------