%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET975+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 12:45:06 PM UTC 2026
% Result : Theorem 0.21s 0.55s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 64 ( 10 unt; 3 def)
% Number of atoms : 139 ( 23 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 132 ( 57 ~; 62 |; 4 &)
% ( 8 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 74 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f3,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f4,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f6,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X0,X2)
& in(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f9,conjecture,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3))
<=> ( X0 = X2
& in(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t128_zfmisc_1) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3))
<=> ( X0 = X2
& in(X1,X3) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f12,plain,
? [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3))
<~> ( X0 = X2
& in(X1,X3) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f14,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f15,plain,
! [X2,X0,X1] :
( X0 != X2
| in(X2,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f3]) ).
fof(f16,plain,
! [X2,X0,X1] :
( X0 = X2
| ~ in(X2,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f3]) ).
fof(f19,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f4]) ).
fof(f21,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f22,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f23,plain,
! [X2,X3,X0,X1] :
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f26,plain,
( ~ in(sK4,sK6)
| sK3 != sK5
| ~ in(ordered_pair(sK3,sK4),cartesian_product2(singleton(sK5),sK6)) ),
inference(cnf_transformation,[],[f12]) ).
fof(f27,plain,
( in(sK4,sK6)
| in(ordered_pair(sK3,sK4),cartesian_product2(singleton(sK5),sK6)) ),
inference(cnf_transformation,[],[f12]) ).
fof(f28,plain,
( sK3 = sK5
| in(ordered_pair(sK3,sK4),cartesian_product2(singleton(sK5),sK6)) ),
inference(cnf_transformation,[],[f12]) ).
fof(f30,plain,
! [X2,X3,X0,X1] :
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f23,f19]) ).
fof(f31,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f22,f19]) ).
fof(f32,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f21,f19]) ).
fof(f33,plain,
( sK3 = sK5
| in(unordered_pair(unordered_pair(sK3,sK4),singleton(sK3)),cartesian_product2(singleton(sK5),sK6)) ),
inference(definition_unfolding,[],[f28,f19]) ).
fof(f34,plain,
( in(sK4,sK6)
| in(unordered_pair(unordered_pair(sK3,sK4),singleton(sK3)),cartesian_product2(singleton(sK5),sK6)) ),
inference(definition_unfolding,[],[f27,f19]) ).
fof(f35,plain,
( ~ in(sK4,sK6)
| sK3 != sK5
| ~ in(unordered_pair(unordered_pair(sK3,sK4),singleton(sK3)),cartesian_product2(singleton(sK5),sK6)) ),
inference(definition_unfolding,[],[f26,f19]) ).
fof(f36,plain,
! [X2,X0] :
( ~ in(X2,singleton(X0))
| X0 = X2 ),
inference(equality_resolution,[],[f16]) ).
fof(f37,plain,
! [X2,X1] :
( in(X2,X1)
| singleton(X2) != X1 ),
inference(equality_resolution,[],[f15]) ).
fof(f38,plain,
! [X2] : in(X2,singleton(X2)),
inference(equality_resolution,[],[f37]) ).
fof(f43,definition,
( spl7_1
<=> in(unordered_pair(unordered_pair(sK3,sK4),singleton(sK3)),cartesian_product2(singleton(sK5),sK6)) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
fof(f44,plain,
( in(unordered_pair(unordered_pair(sK3,sK4),singleton(sK3)),cartesian_product2(singleton(sK5),sK6))
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f45,plain,
( ~ in(unordered_pair(unordered_pair(sK3,sK4),singleton(sK3)),cartesian_product2(singleton(sK5),sK6))
| spl7_1 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f47,definition,
( spl7_2
<=> sK3 = sK5 ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
fof(f48,plain,
( sK3 = sK5
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f49,plain,
( sK3 != sK5
| spl7_2 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f51,definition,
( spl7_3
<=> in(sK4,sK6) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
fof(f52,plain,
( in(sK4,sK6)
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f54,plain,
( ~ spl7_1
| ~ spl7_2
| ~ spl7_3 ),
inference(avatar_split_clause,[],[f35,f51,f47,f43]) ).
fof(f55,plain,
( spl7_1
| spl7_3 ),
inference(avatar_split_clause,[],[f34,f51,f43]) ).
fof(f56,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f33,f47,f43]) ).
fof(f57,plain,
( ~ in(unordered_pair(unordered_pair(sK3,sK4),singleton(sK3)),cartesian_product2(singleton(sK3),sK6))
| spl7_1
| ~ spl7_2 ),
inference(forward_demodulation,[],[f45,f48]) ).
fof(f60,plain,
( ~ in(unordered_pair(singleton(sK3),unordered_pair(sK3,sK4)),cartesian_product2(singleton(sK3),sK6))
| spl7_1
| ~ spl7_2 ),
inference(superposition,[],[f57,f14]) ).
fof(f66,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(forward_demodulation,[],[f31,f14]) ).
fof(f67,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(forward_demodulation,[],[f32,f14]) ).
fof(f76,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,X2)
| ~ in(X1,X3)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3)) ),
inference(forward_demodulation,[],[f30,f14]) ).
fof(f78,plain,
! [X2,X0,X1] :
( ~ in(X0,X1)
| in(unordered_pair(singleton(X2),unordered_pair(X2,X0)),cartesian_product2(singleton(X2),X1)) ),
inference(resolution,[],[f76,f38]) ).
fof(f107,plain,
( ! [X0] : in(unordered_pair(singleton(X0),unordered_pair(X0,sK4)),cartesian_product2(singleton(X0),sK6))
| ~ spl7_3 ),
inference(resolution,[],[f78,f52]) ).
fof(f126,plain,
( $false
| spl7_1
| ~ spl7_2
| ~ spl7_3 ),
inference(backward_subsumption_resolution,[],[f60,f107]) ).
fof(f138,plain,
( spl7_1
| ~ spl7_2
| ~ spl7_3 ),
inference(avatar_contradiction_clause,[],[f126]) ).
fof(f149,plain,
( in(unordered_pair(singleton(sK3),unordered_pair(sK3,sK4)),cartesian_product2(singleton(sK5),sK6))
| ~ spl7_1 ),
inference(forward_demodulation,[],[f44,f14]) ).
fof(f150,plain,
( in(sK4,sK6)
| ~ spl7_1 ),
inference(resolution,[],[f149,f67]) ).
fof(f151,plain,
( in(sK3,singleton(sK5))
| ~ spl7_1 ),
inference(resolution,[],[f149,f66]) ).
fof(f158,plain,
( spl7_3
| ~ spl7_1 ),
inference(avatar_split_clause,[],[f150,f43,f51]) ).
fof(f164,plain,
( sK3 = sK5
| ~ spl7_1 ),
inference(resolution,[],[f151,f36]) ).
fof(f170,plain,
( $false
| ~ spl7_1
| spl7_2 ),
inference(forward_subsumption_resolution,[],[f164,f49]) ).
fof(f171,plain,
( ~ spl7_1
| spl7_2 ),
inference(avatar_contradiction_clause,[],[f170]) ).
cnf(s1,plain,
( ~ spl7_1
| ~ spl7_2
| ~ spl7_3 ),
inference(sat_conversion,[],[f54]) ).
cnf(s2,plain,
( spl7_1
| spl7_3 ),
inference(sat_conversion,[],[f55]) ).
cnf(s3,plain,
( spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f56]) ).
cnf(s4,plain,
( spl7_1
| ~ spl7_2
| ~ spl7_3 ),
inference(sat_conversion,[],[f138]) ).
cnf(s7,plain,
( ~ spl7_1
| spl7_3 ),
inference(sat_conversion,[],[f158]) ).
cnf(s8,plain,
( ~ spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f171]) ).
cnf(s9,plain,
spl7_1,
inference(rat,[],[s4,s2,s3]) ).
cnf(s10,plain,
spl7_2,
inference(rat,[],[s8,s9]) ).
cnf(s11,plain,
spl7_3,
inference(rat,[],[s7,s9]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s1,s10,s11,s9]) ).
fof(f172,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET975+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.16/0.44 % Computer : n005.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Mon Sep 28 03:17:01 UTC 2026
% 0.16/0.45 % CPUTime :
% 0.16/0.45 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.21/0.50 Running first-order model finding
% 0.21/0.50 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.55 % (400214)Will run a generic schedule for satisfiability detection.
% 0.21/0.55 % (400220)% WARNING: option uhcvi not known.
% 0.21/0.55 % (400219)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4061841887_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.55 % TRYING [1]
% 0.21/0.55 % (400220)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=990012446:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.55 % TRYING [2]
% 0.21/0.55 % TRYING [3]
% 0.21/0.55 % TRYING [4]
% 0.21/0.55 % (400220) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-400214-400220"...
% 0.21/0.55 % (400221)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=287650561:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.55 % (400222)dis+10_1_sil=32000:sp=arity:random_seed=245302684:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.55 % (400223)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=894303898:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.55 % (400220)...printing done.
% 0.21/0.55 % (400224)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4017395693:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.55 % (400225)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2279380968:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.55 % (400220)Refutation found. Thanks to Tanya!
% 0.21/0.55 % SZS status Theorem for theBenchmark
% 0.21/0.55 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.55 % (400220)------------------------------
% 0.21/0.55 % (400220)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.55 % (400220)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.55 % (400220)CaDiCaL version: 2.1.3
% 0.21/0.55 % (400220)Termination reason: Refutation
% 0.21/0.55 % (400220)Time elapsed: 0.011 s
% 0.21/0.55 % (400220)Peak memory usage: 13 MB
% 0.21/0.55 % (400220)Instructions burned: 10 (million)
% 0.21/0.55 % (400214)Success in time 0.038 s
% 0.21/0.55 % Vampire exiting
%------------------------------------------------------------------------------