%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET988+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 : n005.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 12:42:28 PM UTC 2026
% Result : Theorem 2.55s 1.31s
% Output : Refutation 2.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 35 ( 4 unt; 0 def)
% Number of atoms : 138 ( 37 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 166 ( 63 ~; 56 |; 35 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-2 aty)
% Number of variables : 110 ( 90 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f31,conjecture,
! [X0] :
( ( ! [X1] :
~ ( in(X1,X0)
& ! [X2,X3] : ordered_pair(X2,X3) != X1 )
& ! [X1,X2,X3] :
( ( in(ordered_pair(X1,X2),X0)
& in(ordered_pair(X1,X3),X0) )
=> X2 = X3 ) )
=> ( relation(X0)
& function(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_funct_1) ).
fof(f32,negated_conjecture,
~ ! [X0] :
( ( ! [X1] :
~ ( in(X1,X0)
& ! [X2,X3] : ordered_pair(X2,X3) != X1 )
& ! [X1,X2,X3] :
( ( in(ordered_pair(X1,X2),X0)
& in(ordered_pair(X1,X3),X0) )
=> X2 = X3 ) )
=> ( relation(X0)
& function(X0) ) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f33,axiom,
! [X0] :
( function(X0)
<=> ! [X1,X2,X3] :
( ( in(ordered_pair(X1,X2),X0)
& in(ordered_pair(X1,X3),X0) )
=> X2 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_1) ).
fof(f34,axiom,
! [X0] :
( relation(X0)
<=> ! [X1] :
~ ( in(X1,X0)
& ! [X2,X3] : X1 != ordered_pair(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
fof(f35,plain,
~ ! [X0] :
( ( ! [X1] :
~ ( in(X1,X0)
& ! [X2,X3] : ordered_pair(X2,X3) != X1 )
& ! [X4,X5,X6] :
( ( in(ordered_pair(X4,X5),X0)
& in(ordered_pair(X4,X6),X0) )
=> X5 = X6 ) )
=> ( relation(X0)
& function(X0) ) ),
inference(rectify,[],[f32]) ).
fof(f36,plain,
? [X0] :
( ( ~ relation(X0)
| ~ function(X0) )
& ! [X1] :
( ~ in(X1,X0)
| ? [X2,X3] : ordered_pair(X2,X3) = X1 )
& ! [X4,X5,X6] :
( X5 = X6
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(ordered_pair(X4,X6),X0) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f37,plain,
? [X0] :
( ( ~ relation(X0)
| ~ function(X0) )
& ! [X1] :
( ~ in(X1,X0)
| ? [X2,X3] : ordered_pair(X2,X3) = X1 )
& ! [X4,X5,X6] :
( X5 = X6
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(ordered_pair(X4,X6),X0) ) ),
inference(flattening,[],[f36]) ).
fof(f40,plain,
! [X0] :
( relation(X0)
<=> ! [X1] :
( ~ in(X1,X0)
| ? [X2,X3] : ordered_pair(X2,X3) = X1 ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f41,plain,
! [X0] :
( function(X0)
<=> ! [X1,X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(ordered_pair(X1,X3),X0) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f42,plain,
! [X0] :
( function(X0)
<=> ! [X1,X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(ordered_pair(X1,X3),X0) ) ),
inference(flattening,[],[f41]) ).
fof(f46,plain,
( ( ~ relation(sK0)
| ~ function(sK0) )
& ! [X1] :
( ~ in(X1,sK0)
| ordered_pair(sK1(X1),sK2(X1)) = X1 )
& ! [X4,X5,X6] :
( X5 = X6
| ~ in(ordered_pair(X4,X5),sK0)
| ~ in(ordered_pair(X4,X6),sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X2,sK1(X1)),skolemize(X3,sK2(X1))],[f37]) ).
fof(f49,plain,
! [X0] :
( ( relation(X0)
| ? [X1] :
( in(X1,X0)
& ! [X2,X3] : ordered_pair(X2,X3) != X1 ) )
& ( ! [X1] :
( ~ in(X1,X0)
| ? [X2,X3] : ordered_pair(X2,X3) = X1 )
| ~ relation(X0) ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f50,plain,
! [X0] :
( ( relation(X0)
| ? [X1] :
( in(X1,X0)
& ! [X2,X3] : ordered_pair(X2,X3) != X1 ) )
& ( ! [X4] :
( ~ in(X4,X0)
| ? [X5,X6] : ordered_pair(X5,X6) = X4 )
| ~ relation(X0) ) ),
inference(rectify,[],[f49]) ).
fof(f51,plain,
! [X0] :
( ( relation(X0)
| ( in(sK5(X0),X0)
& ! [X2,X3] : ordered_pair(X2,X3) != sK5(X0) ) )
& ( ! [X4] :
( ~ in(X4,X0)
| ordered_pair(sK6(X4),sK7(X4)) = X4 )
| ~ relation(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X1,sK5(X0)),skolemize(X5,sK6(X4)),skolemize(X6,sK7(X4))],[f50]) ).
fof(f52,plain,
! [X0] :
( ( function(X0)
| ? [X1,X2,X3] :
( X2 != X3
& in(ordered_pair(X1,X2),X0)
& in(ordered_pair(X1,X3),X0) ) )
& ( ! [X1,X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(ordered_pair(X1,X3),X0) )
| ~ function(X0) ) ),
inference(nnf_transformation,[],[f42]) ).
fof(f53,plain,
! [X0] :
( ( function(X0)
| ? [X1,X2,X3] :
( X2 != X3
& in(ordered_pair(X1,X2),X0)
& in(ordered_pair(X1,X3),X0) ) )
& ( ! [X4,X5,X6] :
( X5 = X6
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(ordered_pair(X4,X6),X0) )
| ~ function(X0) ) ),
inference(rectify,[],[f52]) ).
fof(f54,plain,
! [X0] :
( ( function(X0)
| ( sK9(X0) != sK10(X0)
& in(ordered_pair(sK8(X0),sK9(X0)),X0)
& in(ordered_pair(sK8(X0),sK10(X0)),X0) ) )
& ( ! [X4,X5,X6] :
( X5 = X6
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(ordered_pair(X4,X6),X0) )
| ~ function(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10]),skolemize(X1,sK8(X0)),skolemize(X2,sK9(X0)),skolemize(X3,sK10(X0))],[f53]) ).
fof(f58,plain,
! [X6,X4,X5] :
( ~ in(ordered_pair(X4,X6),sK0)
| ~ in(ordered_pair(X4,X5),sK0)
| X5 = X6 ),
inference(cnf_transformation,[],[f46]) ).
fof(f59,plain,
! [X1] :
( ordered_pair(sK1(X1),sK2(X1)) = X1
| ~ in(X1,sK0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f60,plain,
( ~ function(sK0)
| ~ relation(sK0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f68,plain,
! [X2,X3,X0] :
( ordered_pair(X2,X3) != sK5(X0)
| relation(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f69,plain,
! [X0] :
( in(sK5(X0),X0)
| relation(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f72,plain,
! [X0] :
( in(ordered_pair(sK8(X0),sK10(X0)),X0)
| function(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f73,plain,
! [X0] :
( in(ordered_pair(sK8(X0),sK9(X0)),X0)
| function(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f74,plain,
! [X0] :
( sK9(X0) != sK10(X0)
| function(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f92,plain,
! [X0,X1] :
( sK5(X1) != X0
| relation(X1)
| ~ in(X0,sK0) ),
inference(superposition,[],[f68,f59]) ).
fof(f95,plain,
! [X0] :
( ~ in(ordered_pair(sK8(sK0),X0),sK0)
| function(sK0)
| sK10(sK0) = X0 ),
inference(resolution,[],[f72,f58]) ).
fof(f97,plain,
! [X0] :
( ~ in(sK5(X0),sK0)
| relation(X0) ),
inference(equality_resolution,[],[f92]) ).
fof(f102,plain,
( relation(sK0)
| relation(sK0) ),
inference(resolution,[],[f97,f69]) ).
fof(f103,plain,
relation(sK0),
inference(duplicate_literal_removal,[],[f102]) ).
fof(f108,plain,
( function(sK0)
| sK10(sK0) = sK9(sK0)
| function(sK0) ),
inference(resolution,[],[f95,f73]) ).
fof(f109,plain,
( function(sK0)
| sK10(sK0) = sK9(sK0) ),
inference(duplicate_literal_removal,[],[f108]) ).
fof(f111,plain,
function(sK0),
inference(forward_subsumption_resolution,[],[f109,f74]) ).
fof(f117,plain,
~ relation(sK0),
inference(resolution,[],[f111,f60]) ).
fof(f118,plain,
$false,
inference(forward_subsumption_resolution,[],[f117,f103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET988+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 03:19:47 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 2.55/1.31 % (403677)Detected formulas, will run a generic FOF schedule.
% 2.55/1.31 % (403686)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=930934895:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.55/1.31 % (403686)First to succeed.
% 2.55/1.31 % (403686)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-403677"
% 2.55/1.31 % (403683)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=2893818832:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.55/1.31 % (403685)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2475022428:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.55/1.31 % (403685)Also succeeded, but the first one will report.
% 2.55/1.31 % (403682)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=696291412:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.55/1.31 % (403684)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=1189628246:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.55/1.31 % (403688)dis-21_1_sil=8000:lcm=predicate:random_seed=1748438552: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)
% 2.55/1.31 % (403688)Also succeeded, but the first one will report.
% 2.55/1.31 % (403687)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2979303118:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.55/1.31 % (403687)Also succeeded, but the first one will report.
% 2.55/1.31 % (403686)Refutation found. Thanks to Tanya!
% 2.55/1.31 % SZS status Theorem for theBenchmark
% 2.55/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 2.55/1.31 % (403686)------------------------------
% 2.55/1.31 % (403686)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.31 % (403686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.31 % (403686)CaDiCaL version: 2.1.3
% 2.55/1.31 % (403686)Termination reason: Refutation
% 2.55/1.31 % (403686)Time elapsed: 0.002 s
% 2.55/1.31 % (403686)Peak memory usage: 88 MB
% 2.55/1.31 % (403686)Instructions burned: 4 (million)
% 2.55/1.31 % (403686)------------------------------
% 2.55/1.31 % (403686)------------------------------
% 2.55/1.31 % (403677)Success in time 0.271 s
% 2.55/1.31 % Vampire exiting
%------------------------------------------------------------------------------