%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET616+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 12:41:23 PM UTC 2026
% Result : Theorem 2.02s 0.88s
% Output : Refutation 2.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 30 ( 7 unt; 0 def)
% Number of atoms : 92 ( 22 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 104 ( 42 ~; 41 |; 16 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 48 ( 44 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( member(X2,X0)
& ~ member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(f4,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f7,conjecture,
! [X0,X1] :
( difference(X0,X1) = difference(X1,X0)
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th90) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( difference(X0,X1) = difference(X1,X0)
=> X0 = X1 ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
? [X0,X1] :
( X0 != X1
& difference(X0,X1) = difference(X1,X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f11,plain,
( sK0 != sK1
& difference(sK0,sK1) = difference(sK1,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f9]) ).
fof(f12,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X2] :
( ( member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X1)
| ~ member(X2,X0) ) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f13,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| X0 != X1 ) ),
inference(rectify,[],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ( X0 = X1
| ( ( ~ member(sK2(X0,X1),X1)
| ~ member(sK2(X0,X1),X0) )
& ( member(sK2(X0,X1),X1)
| member(sK2(X0,X1),X0) ) ) )
& ( ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| X0 != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f13]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) )
& ( ( member(X2,X0)
& ~ member(X2,X1) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) )
& ( ( member(X2,X0)
& ~ member(X2,X1) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
difference(sK0,sK1) = difference(sK1,sK0),
inference(cnf_transformation,[],[f11]) ).
fof(f20,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f11]) ).
fof(f23,plain,
! [X0,X1] :
( member(sK2(X0,X1),X1)
| X0 = X1
| member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f24,plain,
! [X0,X1] :
( ~ member(sK2(X0,X1),X1)
| X0 = X1
| ~ member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f27,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f28,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f29,plain,
! [X2,X0,X1] :
( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f33,plain,
! [X0] :
( ~ member(X0,difference(sK0,sK1))
| member(X0,sK1) ),
inference(superposition,[],[f28,f19]) ).
fof(f34,plain,
! [X0] : ~ member(X0,difference(sK0,sK1)),
inference(forward_subsumption_resolution,[],[f33,f27]) ).
fof(f38,plain,
! [X0] :
( member(X0,sK1)
| ~ member(X0,sK0) ),
inference(resolution,[],[f29,f34]) ).
fof(f39,plain,
! [X0] :
( member(X0,difference(sK0,sK1))
| ~ member(X0,sK1)
| member(X0,sK0) ),
inference(superposition,[],[f29,f19]) ).
fof(f40,plain,
! [X0] :
( member(X0,sK0)
| ~ member(X0,sK1) ),
inference(forward_subsumption_resolution,[],[f39,f28]) ).
fof(f50,plain,
! [X0] :
( ~ member(sK2(X0,sK0),sK1)
| ~ member(sK2(X0,sK0),X0)
| sK0 = X0 ),
inference(resolution,[],[f24,f40]) ).
fof(f56,plain,
( ~ member(sK2(sK1,sK0),sK1)
| sK0 = sK1 ),
inference(factoring,[],[f50]) ).
fof(f57,plain,
~ member(sK2(sK1,sK0),sK1),
inference(forward_subsumption_resolution,[],[f56,f20]) ).
fof(f61,plain,
~ member(sK2(sK1,sK0),sK0),
inference(resolution,[],[f57,f38]) ).
fof(f62,plain,
( sK0 = sK1
| member(sK2(sK1,sK0),sK1) ),
inference(resolution,[],[f61,f23]) ).
fof(f64,plain,
member(sK2(sK1,sK0),sK1),
inference(forward_subsumption_resolution,[],[f62,f20]) ).
fof(f65,plain,
$false,
inference(forward_subsumption_resolution,[],[f64,f57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET616+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Mon Sep 28 02:18:49 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.03/0.32 Running first-order theorem proving
% 0.03/0.32 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
% 2.02/0.88 % (2946850)Detected formulas, will run a generic FOF schedule.
% 2.02/0.88 % (2946859)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3460165508:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.02/0.88 % (2946861)dis-21_1_sil=8000:lcm=predicate:random_seed=3196046574: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)
% 2.02/0.88 % (2946856)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=3875981419:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.02/0.88 % (2946860)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2890427719:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.02/0.88 % (2946858)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1546421306:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.02/0.88 % (2946855)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=4102770313:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.02/0.88 % (2946857)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=4018144205:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.02/0.88 % (2946859)First to succeed.
% 2.02/0.88 % (2946859)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2946850"
% 2.02/0.88 % (2946858)Also succeeded, but the first one will report.
% 2.02/0.88 % (2946861)Instruction limit reached!
% 2.02/0.88 % (2946861)------------------------------
% 2.02/0.88 % (2946861)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.02/0.88 % (2946861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.88 % (2946861)CaDiCaL version: 2.1.3
% 2.02/0.88 % (2946861)Termination reason: Instruction limit
% 2.02/0.88 % (2946861)Termination phase: Saturation
% 2.02/0.88 % (2946861)Time elapsed: 0.043 s
% 2.02/0.88 % (2946861)Peak memory usage: 88 MB
% 2.02/0.88 % (2946861)Instructions burned: 130 (million)
% 2.02/0.88 % (2946860)Instruction limit reached!
% 2.02/0.88 % (2946860)------------------------------
% 2.02/0.88 % (2946860)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.02/0.88 % (2946860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.88 % (2946860)CaDiCaL version: 2.1.3
% 2.02/0.88 % (2946860)Termination reason: Instruction limit
% 2.02/0.88 % (2946860)Termination phase: Saturation
% 2.02/0.88 % (2946860)Time elapsed: 0.048 s
% 2.02/0.88 % (2946860)Peak memory usage: 89 MB
% 2.02/0.88 % (2946860)Instructions burned: 141 (million)
% 2.02/0.88 % (2946869)lrs+10_1_sil=8000:sp=occurrence:random_seed=1638768682:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.02/0.88 % (2946869)Also succeeded, but the first one will report.
% 2.02/0.88 % (2946870)lrs+10_1_sil=32000:urr=on:br=off:random_seed=725907534:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 2.02/0.88 % (2946859)Refutation found. Thanks to Tanya!
% 2.02/0.88 % SZS status Theorem for theBenchmark
% 2.02/0.88 % SZS output start Proof for theBenchmark
% See solution above
% 2.02/0.88 % (2946859)------------------------------
% 2.02/0.88 % (2946859)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.02/0.88 % (2946859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.88 % (2946859)CaDiCaL version: 2.1.3
% 2.02/0.88 % (2946859)Termination reason: Refutation
% 2.02/0.88 % (2946859)Time elapsed: 0.001 s
% 2.02/0.88 % (2946859)Peak memory usage: 88 MB
% 2.02/0.88 % (2946859)Instructions burned: 2 (million)
% 2.02/0.88 % (2946859)------------------------------
% 2.02/0.88 % (2946859)------------------------------
% 2.02/0.88 % (2946850)Success in time 0.261 s
% 2.02/0.88 % Vampire exiting
%------------------------------------------------------------------------------