%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET977+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 : n010.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 12:45:07 PM UTC 2026
% Result : Theorem 0.15s 0.44s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 51 ( 12 unt; 2 def)
% Number of atoms : 124 ( 48 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 135 ( 62 ~; 49 |; 17 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 84 ( 0 sgn 80 !; 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] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
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(f9,axiom,
! [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,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3)))
<=> ( in(X0,X2)
& X1 = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t129_zfmisc_1) ).
fof(f11,conjecture,
! [X0,X1] :
( X0 != empty_set
=> ( cartesian_product2(singleton(X1),X0) != empty_set
& cartesian_product2(X0,singleton(X1)) != empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t130_zfmisc_1) ).
fof(f12,negated_conjecture,
~ ! [X0,X1] :
( X0 != empty_set
=> ( cartesian_product2(singleton(X1),X0) != empty_set
& cartesian_product2(X0,singleton(X1)) != empty_set ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f14,plain,
? [X0,X1] :
( ( empty_set = cartesian_product2(singleton(X1),X0)
| empty_set = cartesian_product2(X0,singleton(X1)) )
& X0 != empty_set ),
inference(ennf_transformation,[],[f12]) ).
fof(f15,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f16,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f15]) ).
fof(f17,plain,
! [X0] :
( ( X0 = empty_set
| in(sK0(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f16]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3))
| X0 != X2
| ~ in(X1,X3) )
& ( ( X0 = X2
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f21,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3))
| X0 != X2
| ~ in(X1,X3) )
& ( ( X0 = X2
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) ) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3)))
| ~ in(X0,X2)
| X1 != X3 )
& ( ( in(X0,X2)
& X1 = X3 )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3))) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3)))
| ~ in(X0,X2)
| X1 != X3 )
& ( ( in(X0,X2)
& X1 = X3 )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3))) ) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
( ( empty_set = cartesian_product2(singleton(sK4),sK3)
| empty_set = cartesian_product2(sK3,singleton(sK4)) )
& empty_set != sK3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f14]) ).
fof(f26,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f27,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f17]) ).
fof(f28,plain,
! [X0] :
( in(sK0(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f17]) ).
fof(f29,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f4]) ).
fof(f36,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3))
| X0 != X2
| ~ in(X1,X3) ),
inference(cnf_transformation,[],[f21]) ).
fof(f39,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3)))
| ~ in(X0,X2)
| X1 != X3 ),
inference(cnf_transformation,[],[f23]) ).
fof(f40,plain,
empty_set != sK3,
inference(cnf_transformation,[],[f24]) ).
fof(f41,plain,
( empty_set = cartesian_product2(singleton(sK4),sK3)
| empty_set = cartesian_product2(sK3,singleton(sK4)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f43,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(singleton(X2),X3))
| X0 != X2
| ~ in(X1,X3) ),
inference(definition_unfolding,[],[f36,f29]) ).
fof(f46,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,singleton(X3)))
| ~ in(X0,X2)
| X1 != X3 ),
inference(definition_unfolding,[],[f39,f29]) ).
fof(f49,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f27]) ).
fof(f50,plain,
! [X2,X3,X1] :
( in(unordered_pair(unordered_pair(X2,X1),singleton(X2)),cartesian_product2(singleton(X2),X3))
| ~ in(X1,X3) ),
inference(equality_resolution,[],[f43]) ).
fof(f51,plain,
! [X2,X3,X0] :
( in(unordered_pair(unordered_pair(X0,X3),singleton(X0)),cartesian_product2(X2,singleton(X3)))
| ~ in(X0,X2) ),
inference(equality_resolution,[],[f46]) ).
fof(f56,definition,
( spl5_2
<=> empty_set = cartesian_product2(sK3,singleton(sK4)) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f58,plain,
( empty_set = cartesian_product2(sK3,singleton(sK4))
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f60,definition,
( spl5_3
<=> empty_set = cartesian_product2(singleton(sK4),sK3) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
fof(f62,plain,
( empty_set = cartesian_product2(singleton(sK4),sK3)
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f63,plain,
( spl5_2
| spl5_3 ),
inference(avatar_split_clause,[],[f41,f60,f56]) ).
fof(f196,plain,
! [X2,X3,X1] :
( in(unordered_pair(singleton(X2),unordered_pair(X2,X1)),cartesian_product2(singleton(X2),X3))
| ~ in(X1,X3) ),
inference(forward_demodulation,[],[f50,f26]) ).
fof(f197,plain,
! [X2,X3,X0] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X3)),cartesian_product2(X2,singleton(X3)))
| ~ in(X0,X2) ),
inference(forward_demodulation,[],[f51,f26]) ).
fof(f752,plain,
( ! [X0] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK4)),empty_set)
| ~ in(X0,sK3) )
| ~ spl5_2 ),
inference(superposition,[],[f197,f58]) ).
fof(f753,plain,
( ! [X0] : ~ in(X0,sK3)
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f752,f49]) ).
fof(f754,plain,
( empty_set = sK3
| ~ spl5_2 ),
inference(resolution,[],[f753,f28]) ).
fof(f755,plain,
( $false
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f754,f40]) ).
fof(f756,plain,
~ spl5_2,
inference(avatar_contradiction_clause,[],[f755]) ).
fof(f767,plain,
( ! [X0] :
( in(unordered_pair(singleton(sK4),unordered_pair(sK4,X0)),empty_set)
| ~ in(X0,sK3) )
| ~ spl5_3 ),
inference(superposition,[],[f196,f62]) ).
fof(f770,plain,
( ! [X0] : ~ in(X0,sK3)
| ~ spl5_3 ),
inference(forward_subsumption_resolution,[],[f767,f49]) ).
fof(f771,plain,
( empty_set = sK3
| ~ spl5_3 ),
inference(resolution,[],[f770,f28]) ).
fof(f772,plain,
( $false
| ~ spl5_3 ),
inference(forward_subsumption_resolution,[],[f771,f40]) ).
fof(f773,plain,
~ spl5_3,
inference(avatar_contradiction_clause,[],[f772]) ).
cnf(s23,plain,
( spl5_2
| spl5_3 ),
inference(sat_conversion,[],[f63]) ).
cnf(s442,plain,
~ spl5_2,
inference(sat_conversion,[],[f756]) ).
cnf(s459,plain,
~ spl5_3,
inference(sat_conversion,[],[f773]) ).
cnf(s464,plain,
$false,
inference(rat,[],[s23,s459,s442]) ).
fof(f774,plain,
$false,
inference(avatar_sat_refutation,[],[s464]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET977+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n010.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 03:18:02 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.15/0.39 Running first-order model finding
% 0.15/0.39 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
% 0.15/0.44 % (1530347)Will run a generic schedule for satisfiability detection.
% 0.15/0.44 % (1530354)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1314607985:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.44 % (1530353)% WARNING: option uhcvi not known.
% 0.15/0.44 % (1530352)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=175563064_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.44 % (1530355)dis+10_1_sil=32000:sp=arity:random_seed=4177166057:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.44 % (1530356)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2380434697:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.44 % (1530357)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1173692885:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.44 % (1530358)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2893279255:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.44 % TRYING [1]
% 0.15/0.44 % TRYING [2]
% 0.15/0.44 % (1530353)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2971890592:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.44 % (1530354) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1530347-1530354"...
% 0.15/0.44 % TRYING [3]
% 0.15/0.44 % (1530355) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1530347-1530355"...
% 0.15/0.44 % (1530356) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1530347-1530356"...
% 0.15/0.44 % (1530354)...printing done.
% 0.15/0.44 % (1530358) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1530347-1530358"...
% 0.15/0.44 % (1530354)Refutation found. Thanks to Tanya!
% 0.15/0.44 % SZS status Theorem for theBenchmark
% 0.15/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.45 % (1530354)------------------------------
% 0.15/0.45 % (1530354)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.45 % (1530354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.45 % (1530354)CaDiCaL version: 2.1.3
% 0.15/0.45 % (1530354)Termination reason: Refutation
% 0.15/0.45 % (1530354)Time elapsed: 0.011 s
% 0.15/0.45 % (1530354)Peak memory usage: 12 MB
% 0.15/0.45 % (1530354)Instructions burned: 26 (million)
% 0.15/0.45 % (1530347)Success in time 0.046 s
% 0.15/0.45 % Vampire exiting
%------------------------------------------------------------------------------