%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU267+1 : TPTP v9.3.1. Released v3.3.0.
% 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 12:48:05 PM UTC 2026
% Result : Theorem 2.57s 1.13s
% Output : Refutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 7 unt; 2 def)
% Number of atoms : 124 ( 103 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 140 ( 57 ~; 53 |; 14 &)
% ( 8 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 122 ( 0 sgn 104 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,conjecture,
! [X0,X1] :
( pair_first(ordered_pair(X0,X1)) = X0
& pair_second(ordered_pair(X0,X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_mcart_1) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( pair_first(ordered_pair(X0,X1)) = X0
& pair_second(ordered_pair(X0,X1)) = X1 ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,axiom,
! [X0] :
( ? [X1,X2] : X0 = ordered_pair(X1,X2)
=> ! [X1] :
( X1 = pair_first(X0)
<=> ! [X2,X3] :
( X0 = ordered_pair(X2,X3)
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_mcart_1) ).
fof(f20,axiom,
! [X0] :
( ? [X1,X2] : X0 = ordered_pair(X1,X2)
=> ! [X1] :
( X1 = pair_second(X0)
<=> ! [X2,X3] :
( X0 = ordered_pair(X2,X3)
=> X1 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_mcart_1) ).
fof(f21,plain,
! [X0] :
( ? [X1,X2] : X0 = ordered_pair(X1,X2)
=> ! [X3] :
( pair_first(X0) = X3
<=> ! [X4,X5] :
( ordered_pair(X4,X5) = X0
=> X3 = X4 ) ) ),
inference(rectify,[],[f19]) ).
fof(f22,plain,
! [X0] :
( ? [X1,X2] : X0 = ordered_pair(X1,X2)
=> ! [X3] :
( pair_second(X0) = X3
<=> ! [X4,X5] :
( ordered_pair(X4,X5) = X0
=> X3 = X5 ) ) ),
inference(rectify,[],[f20]) ).
fof(f30,plain,
? [X0,X1] :
( pair_first(ordered_pair(X0,X1)) != X0
| pair_second(ordered_pair(X0,X1)) != X1 ),
inference(ennf_transformation,[],[f18]) ).
fof(f31,plain,
! [X0] :
( ! [X3] :
( pair_first(X0) = X3
<=> ! [X4,X5] :
( X3 = X4
| ordered_pair(X4,X5) != X0 ) )
| ! [X1,X2] : ordered_pair(X1,X2) != X0 ),
inference(ennf_transformation,[],[f21]) ).
fof(f32,plain,
! [X0] :
( ! [X3] :
( pair_second(X0) = X3
<=> ! [X4,X5] :
( X3 = X5
| ordered_pair(X4,X5) != X0 ) )
| ! [X1,X2] : ordered_pair(X1,X2) != X0 ),
inference(ennf_transformation,[],[f22]) ).
fof(f36,plain,
( sK3 != pair_first(ordered_pair(sK3,sK4))
| sK4 != pair_second(ordered_pair(sK3,sK4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f30]) ).
fof(f37,plain,
! [X0] :
( ! [X3] :
( ( pair_first(X0) = X3
| ? [X4,X5] :
( X3 != X4
& ordered_pair(X4,X5) = X0 ) )
& ( ! [X4,X5] :
( X3 = X4
| ordered_pair(X4,X5) != X0 )
| pair_first(X0) != X3 ) )
| ! [X1,X2] : ordered_pair(X1,X2) != X0 ),
inference(nnf_transformation,[],[f31]) ).
fof(f38,plain,
! [X0] :
( ! [X1] :
( ( pair_first(X0) = X1
| ? [X2,X3] :
( X1 != X2
& ordered_pair(X2,X3) = X0 ) )
& ( ! [X4,X5] :
( X1 = X4
| ordered_pair(X4,X5) != X0 )
| pair_first(X0) != X1 ) )
| ! [X6,X7] : ordered_pair(X6,X7) != X0 ),
inference(rectify,[],[f37]) ).
fof(f39,plain,
! [X0] :
( ! [X1] :
( ( pair_first(X0) = X1
| ( sK5(X0,X1) != X1
& ordered_pair(sK5(X0,X1),sK6(X0,X1)) = X0 ) )
& ( ! [X4,X5] :
( X1 = X4
| ordered_pair(X4,X5) != X0 )
| pair_first(X0) != X1 ) )
| ! [X6,X7] : ordered_pair(X6,X7) != X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X2,sK5(X0,X1)),skolemize(X3,sK6(X0,X1))],[f38]) ).
fof(f40,plain,
! [X0] :
( ! [X3] :
( ( pair_second(X0) = X3
| ? [X4,X5] :
( X3 != X5
& ordered_pair(X4,X5) = X0 ) )
& ( ! [X4,X5] :
( X3 = X5
| ordered_pair(X4,X5) != X0 )
| pair_second(X0) != X3 ) )
| ! [X1,X2] : ordered_pair(X1,X2) != X0 ),
inference(nnf_transformation,[],[f32]) ).
fof(f41,plain,
! [X0] :
( ! [X1] :
( ( pair_second(X0) = X1
| ? [X2,X3] :
( X1 != X3
& ordered_pair(X2,X3) = X0 ) )
& ( ! [X4,X5] :
( X1 = X5
| ordered_pair(X4,X5) != X0 )
| pair_second(X0) != X1 ) )
| ! [X6,X7] : ordered_pair(X6,X7) != X0 ),
inference(rectify,[],[f40]) ).
fof(f42,plain,
! [X0] :
( ! [X1] :
( ( pair_second(X0) = X1
| ( sK8(X0,X1) != X1
& ordered_pair(sK7(X0,X1),sK8(X0,X1)) = X0 ) )
& ( ! [X4,X5] :
( X1 = X5
| ordered_pair(X4,X5) != X0 )
| pair_second(X0) != X1 ) )
| ! [X6,X7] : ordered_pair(X6,X7) != X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X2,sK7(X0,X1)),skolemize(X3,sK8(X0,X1))],[f41]) ).
fof(f54,plain,
( sK3 != pair_first(ordered_pair(sK3,sK4))
| sK4 != pair_second(ordered_pair(sK3,sK4)) ),
inference(cnf_transformation,[],[f36]) ).
fof(f55,plain,
! [X0,X1,X6,X7,X4,X5] :
( X1 = X4
| ordered_pair(X4,X5) != X0
| pair_first(X0) != X1
| ordered_pair(X6,X7) != X0 ),
inference(cnf_transformation,[],[f39]) ).
fof(f58,plain,
! [X0,X1,X6,X7,X4,X5] :
( X1 = X5
| ordered_pair(X4,X5) != X0
| pair_second(X0) != X1
| ordered_pair(X6,X7) != X0 ),
inference(cnf_transformation,[],[f42]) ).
fof(f63,plain,
! [X1,X6,X7,X4,X5] :
( X1 = X4
| pair_first(ordered_pair(X4,X5)) != X1
| ordered_pair(X4,X5) != ordered_pair(X6,X7) ),
inference(equality_resolution,[],[f55]) ).
fof(f64,plain,
! [X6,X7,X4,X5] :
( pair_first(ordered_pair(X4,X5)) = X4
| ordered_pair(X4,X5) != ordered_pair(X6,X7) ),
inference(equality_resolution,[],[f63]) ).
fof(f67,plain,
! [X1,X6,X7,X4,X5] :
( X1 = X5
| pair_second(ordered_pair(X4,X5)) != X1
| ordered_pair(X4,X5) != ordered_pair(X6,X7) ),
inference(equality_resolution,[],[f58]) ).
fof(f68,plain,
! [X6,X7,X4,X5] :
( ordered_pair(X4,X5) != ordered_pair(X6,X7)
| pair_second(ordered_pair(X4,X5)) = X5 ),
inference(equality_resolution,[],[f67]) ).
fof(f70,definition,
( spl9_1
<=> sK4 = pair_second(ordered_pair(sK3,sK4)) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
fof(f72,plain,
( sK4 != pair_second(ordered_pair(sK3,sK4))
| spl9_1 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f74,definition,
( spl9_2
<=> sK3 = pair_first(ordered_pair(sK3,sK4)) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
fof(f76,plain,
( sK3 != pair_first(ordered_pair(sK3,sK4))
| spl9_2 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f77,plain,
( ~ spl9_1
| ~ spl9_2 ),
inference(avatar_split_clause,[],[f54,f74,f70]) ).
fof(f84,plain,
! [X0,X1] : pair_second(ordered_pair(X0,X1)) = X1,
inference(equality_resolution,[],[f68]) ).
fof(f94,plain,
( sK4 != sK4
| spl9_1 ),
inference(superposition,[],[f72,f84]) ).
fof(f95,plain,
( $false
| spl9_1 ),
inference(trivial_inequality_removal,[],[f94]) ).
fof(f96,plain,
spl9_1,
inference(avatar_contradiction_clause,[],[f95]) ).
fof(f98,plain,
( ! [X0,X1] :
( sK3 != sK3
| ordered_pair(X0,X1) != ordered_pair(sK3,sK4) )
| spl9_2 ),
inference(superposition,[],[f76,f64]) ).
fof(f99,plain,
( ! [X0,X1] : ordered_pair(X0,X1) != ordered_pair(sK3,sK4)
| spl9_2 ),
inference(trivial_inequality_removal,[],[f98]) ).
fof(f101,plain,
( $false
| spl9_2 ),
inference(equality_resolution,[],[f99]) ).
fof(f102,plain,
spl9_2,
inference(avatar_contradiction_clause,[],[f101]) ).
cnf(s1,plain,
( ~ spl9_1
| ~ spl9_2 ),
inference(sat_conversion,[],[f77]) ).
cnf(s2,plain,
spl9_1,
inference(sat_conversion,[],[f96]) ).
cnf(s3,plain,
spl9_2,
inference(sat_conversion,[],[f102]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f103,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU267+1 : TPTP v9.3.1. Released v3.3.0.
% 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 04:27:39 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 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
% 2.57/1.13 % (2988673)Detected formulas, will run a generic FOF schedule.
% 2.57/1.13 % (2988683)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1968840673:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.57/1.13 % (2988683)First to succeed.
% 2.57/1.13 % (2988680)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=1706609847:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.57/1.13 % (2988682)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3319907493:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.57/1.13 % (2988684)dis-21_1_sil=8000:lcm=predicate:random_seed=697855782: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)
% 2.57/1.13 % (2988678)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=3233789801:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.57/1.13 % (2988681)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4222736321:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.57/1.13 % (2988679)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=2785020763:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.57/1.13 % (2988683)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2988673"
% 2.57/1.13 % (2988682)Also succeeded, but the first one will report.
% 2.57/1.13 % (2988681)Refutation not found, incomplete strategy
% 2.57/1.13 % (2988681)------------------------------
% 2.57/1.13 % (2988681)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.13 % (2988681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.13 % (2988681)CaDiCaL version: 2.1.3
% 2.57/1.13 % (2988681)Termination reason: Refutation not found, incomplete strategy
% 2.57/1.13 % (2988681)Time elapsed: 0.001 s
% 2.57/1.13 % (2988681)Peak memory usage: 88 MB
% 2.57/1.13 % (2988684)Also succeeded, but the first one will report.
% 2.57/1.13 % (2988683)Refutation found. Thanks to Tanya!
% 2.57/1.13 % SZS status Theorem for theBenchmark
% 2.57/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 2.69/1.13 % (2988683)------------------------------
% 2.69/1.13 % (2988683)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.13 % (2988683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.13 % (2988683)CaDiCaL version: 2.1.3
% 2.69/1.13 % (2988683)Termination reason: Refutation
% 2.69/1.13 % (2988683)Time elapsed: 0.003 s
% 2.69/1.13 % (2988683)Peak memory usage: 89 MB
% 2.69/1.13 % (2988683)Instructions burned: 4 (million)
% 2.69/1.13 % (2988683)------------------------------
% 2.69/1.13 % (2988683)------------------------------
% 2.69/1.13 % (2988673)Success in time 0.317 s
% 2.69/1.13 % Vampire exiting
%------------------------------------------------------------------------------