%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN074+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 01:49:14 PM UTC 2026
% Result : Theorem 2.74s 1.18s
% Output : Refutation 2.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 5
% Syntax : Number of formulae : 45 ( 12 unt; 3 def)
% Number of atoms : 126 ( 65 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 132 ( 51 ~; 57 |; 16 &)
% ( 7 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 44 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0,X1] :
! [X2,X3] :
( big_f(X2,X3)
<=> ( X2 = X0
& X3 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel51_1) ).
fof(f2,conjecture,
? [X0] :
! [X1] :
( ? [X2] :
! [X3] :
( big_f(X1,X3)
<=> X3 = X2 )
<=> X1 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel51) ).
fof(f3,negated_conjecture,
~ ? [X0] :
! [X1] :
( ? [X2] :
! [X3] :
( big_f(X1,X3)
<=> X3 = X2 )
<=> X1 = X0 ),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f4,plain,
! [X0] :
? [X1] :
( ? [X2] :
! [X3] :
( big_f(X1,X3)
<=> X3 = X2 )
<~> X1 = X0 ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
! [X0] :
? [X1] :
( ( X0 != X1
| ! [X2] :
? [X3] :
( ( X2 != X3
| ~ big_f(X1,X3) )
& ( X3 = X2
| big_f(X1,X3) ) ) )
& ( X1 = X0
| ? [X2] :
! [X3] :
( ( big_f(X1,X3)
| X2 != X3 )
& ( X3 = X2
| ~ big_f(X1,X3) ) ) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f6,plain,
! [X0] :
? [X1] :
( ( X0 != X1
| ! [X2] :
? [X3] :
( ( X2 != X3
| ~ big_f(X1,X3) )
& ( X3 = X2
| big_f(X1,X3) ) ) )
& ( X1 = X0
| ? [X4] :
! [X5] :
( ( big_f(X1,X5)
| X4 != X5 )
& ( X4 = X5
| ~ big_f(X1,X5) ) ) ) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
! [X0] :
( ( sK0(X0) != X0
| ! [X2] :
( ( sK1(X0,X2) != X2
| ~ big_f(sK0(X0),sK1(X0,X2)) )
& ( sK1(X0,X2) = X2
| big_f(sK0(X0),sK1(X0,X2)) ) ) )
& ( sK0(X0) = X0
| ! [X5] :
( ( big_f(sK0(X0),X5)
| sK2(X0) != X5 )
& ( sK2(X0) = X5
| ~ big_f(sK0(X0),X5) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X1,sK0(X0)),skolemize(X3,sK1(X0,X2)),skolemize(X4,sK2(X0))],[f6]) ).
fof(f8,plain,
? [X0,X1] :
! [X2,X3] :
( ( big_f(X2,X3)
| X0 != X2
| X1 != X3 )
& ( ( X2 = X0
& X3 = X1 )
| ~ big_f(X2,X3) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f9,plain,
? [X0,X1] :
! [X2,X3] :
( ( big_f(X2,X3)
| X0 != X2
| X1 != X3 )
& ( ( X2 = X0
& X3 = X1 )
| ~ big_f(X2,X3) ) ),
inference(flattening,[],[f8]) ).
fof(f10,plain,
! [X2,X3] :
( ( big_f(X2,X3)
| sK3 != X2
| sK4 != X3 )
& ( ( sK3 = X2
& sK4 = X3 )
| ~ big_f(X2,X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f9]) ).
fof(f12,plain,
! [X0,X5] :
( sK0(X0) = X0
| big_f(sK0(X0),X5)
| sK2(X0) != X5 ),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
! [X2,X0] :
( sK0(X0) != X0
| sK1(X0,X2) = X2
| big_f(sK0(X0),sK1(X0,X2)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f14,plain,
! [X2,X0] :
( sK1(X0,X2) != X2
| sK0(X0) != X0
| ~ big_f(sK0(X0),sK1(X0,X2)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f15,plain,
! [X2,X3] :
( ~ big_f(X2,X3)
| sK4 = X3 ),
inference(cnf_transformation,[],[f10]) ).
fof(f16,plain,
! [X2,X3] :
( ~ big_f(X2,X3)
| sK3 = X2 ),
inference(cnf_transformation,[],[f10]) ).
fof(f17,plain,
! [X2,X3] :
( big_f(X2,X3)
| sK3 != X2
| sK4 != X3 ),
inference(cnf_transformation,[],[f10]) ).
fof(f18,definition,
~ sP5(sK3),
introduced(definition,[new_symbols(definition,[sP5])],[inequality_splitting_name_introduction]) ).
fof(f19,definition,
~ sP6(sK4),
introduced(definition,[new_symbols(definition,[sP6])],[inequality_splitting_name_introduction]) ).
fof(f20,plain,
! [X2,X3] :
( big_f(X2,X3)
| sP5(X2)
| sP6(X3) ),
inference(inequality_splitting,[],[f17,f19,f18]) ).
fof(f21,plain,
! [X0] :
( big_f(sK0(X0),sK2(X0))
| sK0(X0) = X0 ),
inference(equality_resolution,[],[f12]) ).
fof(f23,plain,
! [X0] :
( sK0(X0) = sK3
| sK0(X0) = X0 ),
inference(resolution,[],[f21,f16]) ).
fof(f32,plain,
! [X0] :
( sK3 != X0
| sK0(X0) = X0 ),
inference(equality_factoring,[],[f23]) ).
fof(f35,plain,
sK3 = sK0(sK3),
inference(equality_resolution,[],[f32]) ).
fof(f56,plain,
! [X0] :
( sK3 != sK3
| sK1(sK3,X0) = X0
| big_f(sK3,sK1(sK3,X0)) ),
inference(superposition,[],[f13,f35]) ).
fof(f57,plain,
! [X0] :
( big_f(sK3,sK1(sK3,X0))
| sK1(sK3,X0) = X0 ),
inference(trivial_inequality_removal,[],[f56]) ).
fof(f71,definition,
( spl7_5
<=> big_f(sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition]) ).
fof(f72,plain,
( ~ big_f(sK3,sK4)
| spl7_5 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f73,plain,
( big_f(sK3,sK4)
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f103,plain,
! [X0] :
( sK4 = sK1(sK3,X0)
| sK1(sK3,X0) = X0 ),
inference(resolution,[],[f57,f15]) ).
fof(f115,plain,
! [X0] :
( sK4 != X0
| sK1(sK3,X0) = X0 ),
inference(equality_factoring,[],[f103]) ).
fof(f130,plain,
sK4 = sK1(sK3,sK4),
inference(equality_resolution,[],[f115]) ).
fof(f138,plain,
( sK4 != sK4
| sK3 != sK0(sK3)
| ~ big_f(sK0(sK3),sK4) ),
inference(superposition,[],[f14,f130]) ).
fof(f139,plain,
( sK3 != sK0(sK3)
| ~ big_f(sK0(sK3),sK4) ),
inference(trivial_inequality_removal,[],[f138]) ).
fof(f140,plain,
~ big_f(sK0(sK3),sK4),
inference(forward_subsumption_resolution,[],[f139,f16]) ).
fof(f141,plain,
~ big_f(sK3,sK4),
inference(forward_demodulation,[],[f140,f35]) ).
fof(f142,plain,
( $false
| ~ spl7_5 ),
inference(forward_subsumption_resolution,[],[f141,f73]) ).
fof(f143,plain,
~ spl7_5,
inference(avatar_contradiction_clause,[],[f142]) ).
fof(f144,plain,
( sP5(sK3)
| sP6(sK4)
| spl7_5 ),
inference(resolution,[],[f72,f20]) ).
fof(f146,plain,
( sP6(sK4)
| spl7_5 ),
inference(forward_subsumption_resolution,[],[f144,f18]) ).
fof(f147,plain,
( $false
| spl7_5 ),
inference(forward_subsumption_resolution,[],[f146,f19]) ).
fof(f148,plain,
spl7_5,
inference(avatar_contradiction_clause,[],[f147]) ).
cnf(s7,plain,
~ spl7_5,
inference(sat_conversion,[],[f143]) ).
cnf(s8,plain,
spl7_5,
inference(sat_conversion,[],[f148]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s7,s8]) ).
fof(f149,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN074+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 % Computer : n016.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Mon Sep 28 15:37:04 UTC 2026
% 0.07/0.21 % CPUTime :
% 0.07/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.24 Running first-order theorem proving
% 0.07/0.24 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
% 2.74/1.18 % (3712136)Detected formulas, will run a generic FOF schedule.
% 2.74/1.18 % (3712144)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4263940641:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.74/1.18 % (3712144)First to succeed.
% 2.74/1.18 % (3712144)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3712136"
% 2.74/1.18 % (3712146)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3143385386:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.74/1.18 % (3712145)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1353340538:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.74/1.18 % (3712142)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=1190130800:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.74/1.18 % (3712143)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=2750683114:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.74/1.18 % (3712147)dis-21_1_sil=8000:lcm=predicate:random_seed=2300358503: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)
% 2.74/1.18 % (3712141)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=118224898:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.74/1.18 % (3712145)Also succeeded, but the first one will report.
% 2.74/1.18 % (3712146)Also succeeded, but the first one will report.
% 2.74/1.18 % (3712147)Instruction limit reached!
% 2.74/1.18 % (3712147)------------------------------
% 2.74/1.18 % (3712147)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.18 % (3712147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.18 % (3712147)CaDiCaL version: 2.1.3
% 2.74/1.18 % (3712147)Termination reason: Instruction limit
% 2.74/1.18 % (3712147)Termination phase: Saturation
% 2.74/1.18 % (3712147)Time elapsed: 0.068 s
% 2.74/1.18 % (3712147)Peak memory usage: 88 MB
% 2.74/1.18 % (3712147)Instructions burned: 129 (million)
% 2.74/1.18 % (3712144)Refutation found. Thanks to Tanya!
% 2.74/1.18 % SZS status Theorem for theBenchmark
% 2.74/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 2.74/1.19 % (3712144)------------------------------
% 2.74/1.19 % (3712144)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.19 % (3712144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.19 % (3712144)CaDiCaL version: 2.1.3
% 2.74/1.19 % (3712144)Termination reason: Refutation
% 2.74/1.19 % (3712144)Time elapsed: 0.003 s
% 2.74/1.19 % (3712144)Peak memory usage: 89 MB
% 2.74/1.19 % (3712144)Instructions burned: 5 (million)
% 2.74/1.19 % (3712144)------------------------------
% 2.74/1.19 % (3712144)------------------------------
% 2.74/1.19 % (3712136)Success in time 0.295 s
% 2.74/1.19 % Vampire exiting
%------------------------------------------------------------------------------