%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU267+2 : TPTP v9.3.1. Released v3.3.0.
% 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 12:48:05 PM UTC 2026
% Result : Theorem 2.84s 1.37s
% Output : Refutation 2.84s
% 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(f26,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/sandbox/benchmark/theBenchmark.p',d1_mcart_1) ).
fof(f36,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/sandbox/benchmark/theBenchmark.p',d2_mcart_1) ).
fof(f325,conjecture,
! [X0,X1] :
( pair_first(ordered_pair(X0,X1)) = X0
& pair_second(ordered_pair(X0,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_mcart_1) ).
fof(f326,negated_conjecture,
~ ! [X0,X1] :
( pair_first(ordered_pair(X0,X1)) = X0
& pair_second(ordered_pair(X0,X1)) = X1 ),
inference(negated_conjecture,[status(cth)],[f325]) ).
fof(f344,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,[],[f26]) ).
fof(f345,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,[],[f36]) ).
fof(f384,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,[],[f344]) ).
fof(f389,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,[],[f345]) ).
fof(f667,plain,
? [X0,X1] :
( pair_first(ordered_pair(X0,X1)) != X0
| pair_second(ordered_pair(X0,X1)) != X1 ),
inference(ennf_transformation,[],[f326]) ).
fof(f724,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,[],[f384]) ).
fof(f725,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,[],[f724]) ).
fof(f726,plain,
! [X0] :
( ! [X1] :
( ( pair_first(X0) = X1
| ( sK20(X0,X1) != X1
& ordered_pair(sK20(X0,X1),sK21(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,[sK20,sK21]),skolemize(X2,sK20(X0,X1)),skolemize(X3,sK21(X0,X1))],[f725]) ).
fof(f750,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,[],[f389]) ).
fof(f751,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,[],[f750]) ).
fof(f752,plain,
! [X0] :
( ! [X1] :
( ( pair_second(X0) = X1
| ( sK34(X0,X1) != X1
& ordered_pair(sK33(X0,X1),sK34(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,[sK33,sK34]),skolemize(X2,sK33(X0,X1)),skolemize(X3,sK34(X0,X1))],[f751]) ).
fof(f945,plain,
( sK132 != pair_first(ordered_pair(sK132,sK133))
| sK133 != pair_second(ordered_pair(sK132,sK133)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK132,sK133]),skolemize(X0,sK132),skolemize(X1,sK133)],[f667]) ).
fof(f1033,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,[],[f726]) ).
fof(f1069,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,[],[f752]) ).
fof(f1622,plain,
( sK132 != pair_first(ordered_pair(sK132,sK133))
| sK133 != pair_second(ordered_pair(sK132,sK133)) ),
inference(cnf_transformation,[],[f945]) ).
fof(f1685,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,[],[f1033]) ).
fof(f1686,plain,
! [X6,X7,X4,X5] :
( pair_first(ordered_pair(X4,X5)) = X4
| ordered_pair(X4,X5) != ordered_pair(X6,X7) ),
inference(equality_resolution,[],[f1685]) ).
fof(f1706,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,[],[f1069]) ).
fof(f1707,plain,
! [X6,X7,X4,X5] :
( ordered_pair(X4,X5) != ordered_pair(X6,X7)
| pair_second(ordered_pair(X4,X5)) = X5 ),
inference(equality_resolution,[],[f1706]) ).
fof(f1774,definition,
( spl137_1
<=> sK133 = pair_second(ordered_pair(sK132,sK133)) ),
introduced(definition,[new_symbols(definition,[spl137_1])],[avatar_definition]) ).
fof(f1776,plain,
( sK133 != pair_second(ordered_pair(sK132,sK133))
| spl137_1 ),
inference(avatar_component_clause,[],[f1774]) ).
fof(f1778,definition,
( spl137_2
<=> sK132 = pair_first(ordered_pair(sK132,sK133)) ),
introduced(definition,[new_symbols(definition,[spl137_2])],[avatar_definition]) ).
fof(f1780,plain,
( sK132 != pair_first(ordered_pair(sK132,sK133))
| spl137_2 ),
inference(avatar_component_clause,[],[f1778]) ).
fof(f1781,plain,
( ~ spl137_1
| ~ spl137_2 ),
inference(avatar_split_clause,[],[f1622,f1778,f1774]) ).
fof(f1843,plain,
! [X0,X1] : pair_second(ordered_pair(X0,X1)) = X1,
inference(equality_resolution,[],[f1707]) ).
fof(f2743,plain,
( sK133 != sK133
| spl137_1 ),
inference(superposition,[],[f1776,f1843]) ).
fof(f2744,plain,
( $false
| spl137_1 ),
inference(trivial_inequality_removal,[],[f2743]) ).
fof(f2745,plain,
spl137_1,
inference(avatar_contradiction_clause,[],[f2744]) ).
fof(f2749,plain,
( ! [X0,X1] :
( sK132 != sK132
| ordered_pair(X0,X1) != ordered_pair(sK132,sK133) )
| spl137_2 ),
inference(superposition,[],[f1780,f1686]) ).
fof(f2750,plain,
( ! [X0,X1] : ordered_pair(X0,X1) != ordered_pair(sK132,sK133)
| spl137_2 ),
inference(trivial_inequality_removal,[],[f2749]) ).
fof(f2754,plain,
( $false
| spl137_2 ),
inference(equality_resolution,[],[f2750]) ).
fof(f2755,plain,
spl137_2,
inference(avatar_contradiction_clause,[],[f2754]) ).
cnf(s1,plain,
( ~ spl137_1
| ~ spl137_2 ),
inference(sat_conversion,[],[f1781]) ).
cnf(s7,plain,
spl137_1,
inference(sat_conversion,[],[f2745]) ).
cnf(s8,plain,
spl137_2,
inference(sat_conversion,[],[f2755]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s8,s7]) ).
fof(f2756,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU267+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n008.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 04:24:54 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.84/1.37 % (1870088)Detected formulas, will run a generic FOF schedule.
% 2.84/1.37 % (1870098)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2126896530:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.84/1.37 % (1870098)First to succeed.
% 2.84/1.37 % (1870098)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1870088"
% 2.84/1.37 % (1870096)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2311721555:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.84/1.37 % (1870095)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=3021317601:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.84/1.37 % (1870094)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=4100003266:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.84/1.37 % (1870093)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=689665839:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.84/1.37 % (1870097)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2428339146:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.84/1.37 % (1870099)dis-21_1_sil=8000:lcm=predicate:random_seed=2572862890: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)
% 2.84/1.37 % (1870096)Instruction limit reached!
% 2.84/1.37 % (1870096)------------------------------
% 2.84/1.37 % (1870096)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.84/1.37 % (1870096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.84/1.37 % (1870096)CaDiCaL version: 2.1.3
% 2.84/1.37 % (1870096)Termination reason: Instruction limit
% 2.84/1.37 % (1870096)Termination phase: Saturation
% 2.84/1.37 % (1870096)Time elapsed: 0.069 s
% 2.84/1.37 % (1870096)Peak memory usage: 90 MB
% 2.84/1.37 % (1870096)Instructions burned: 110 (million)
% 2.84/1.37 % (1870097)Instruction limit reached!
% 2.84/1.37 % (1870097)------------------------------
% 2.84/1.37 % (1870097)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.84/1.37 % (1870097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.84/1.37 % (1870097)CaDiCaL version: 2.1.3
% 2.84/1.37 % (1870097)Termination reason: Instruction limit
% 2.84/1.37 % (1870097)Termination phase: Saturation
% 2.84/1.37 % (1870097)Time elapsed: 0.080 s
% 2.84/1.37 % (1870097)Peak memory usage: 90 MB
% 2.84/1.37 % (1870097)Instructions burned: 119 (million)
% 2.84/1.37 % (1870099)Instruction limit reached!
% 2.84/1.37 % (1870099)------------------------------
% 2.84/1.37 % (1870099)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.84/1.37 % (1870099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.84/1.37 % (1870099)CaDiCaL version: 2.1.3
% 2.84/1.37 % (1870099)Termination reason: Instruction limit
% 2.84/1.37 % (1870099)Termination phase: Saturation
% 2.84/1.37 % (1870099)Time elapsed: 0.076 s
% 2.84/1.37 % (1870099)Peak memory usage: 90 MB
% 2.84/1.37 % (1870099)Instructions burned: 129 (million)
% 2.84/1.37 % (1870098)Refutation found. Thanks to Tanya!
% 2.84/1.37 % SZS status Theorem for theBenchmark
% 2.84/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 2.84/1.37 % (1870098)------------------------------
% 2.84/1.37 % (1870098)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.84/1.37 % (1870098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.84/1.37 % (1870098)CaDiCaL version: 2.1.3
% 2.84/1.37 % (1870098)Termination reason: Refutation
% 2.84/1.37 % (1870098)Time elapsed: 0.032 s
% 2.84/1.37 % (1870098)Peak memory usage: 91 MB
% 2.84/1.37 % (1870098)Instructions burned: 87 (million)
% 2.84/1.37 % (1870098)------------------------------
% 2.84/1.37 % (1870098)------------------------------
% 2.84/1.37 % (1870088)Success in time 0.326 s
% 2.84/1.37 % Vampire exiting
%------------------------------------------------------------------------------