%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET878+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 : n020.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 12:44:54 PM UTC 2026
% Result : Theorem 0.13s 0.68s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 11 unt; 0 def)
% Number of atoms : 26 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 18 ( 9 ~; 6 |; 0 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 33 ( 31 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f4,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X0
| X3 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(f6,axiom,
! [X0,X1] :
( in(X0,X1)
=> set_intersection2(X1,singleton(X0)) = singleton(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_zfmisc_1) ).
fof(f9,conjecture,
! [X0,X1] : set_intersection2(singleton(X0),unordered_pair(X0,X1)) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_zfmisc_1) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] : set_intersection2(singleton(X0),unordered_pair(X0,X1)) = singleton(X0),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f13,plain,
! [X0,X1] :
( set_intersection2(X1,singleton(X0)) = singleton(X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f14,plain,
? [X0,X1] : singleton(X0) != set_intersection2(singleton(X0),unordered_pair(X0,X1)),
inference(ennf_transformation,[],[f10]) ).
fof(f17,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f23,plain,
! [X2,X3,X0,X1] :
( X0 != X3
| in(X3,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f4]) ).
fof(f25,plain,
! [X0,X1] :
( ~ in(X0,X1)
| singleton(X0) = set_intersection2(X1,singleton(X0)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f28,plain,
singleton(sK3) != set_intersection2(singleton(sK3),unordered_pair(sK3,sK4)),
inference(cnf_transformation,[],[f14]) ).
fof(f29,plain,
! [X2,X3,X1] :
( in(X3,X2)
| unordered_pair(X3,X1) != X2 ),
inference(equality_resolution,[],[f23]) ).
fof(f30,plain,
! [X3,X1] : in(X3,unordered_pair(X3,X1)),
inference(equality_resolution,[],[f29]) ).
fof(f38,plain,
! [X0,X1] : singleton(X0) = set_intersection2(unordered_pair(X0,X1),singleton(X0)),
inference(resolution,[],[f25,f30]) ).
fof(f41,plain,
! [X0,X1] : singleton(X0) = set_intersection2(singleton(X0),unordered_pair(X0,X1)),
inference(forward_demodulation,[],[f38,f17]) ).
fof(f50,plain,
singleton(sK3) != singleton(sK3),
inference(superposition,[],[f28,f41]) ).
fof(f51,plain,
$false,
inference(trivial_inequality_removal,[],[f50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET878+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.59 % Computer : n020.cluster.edu
% 0.09/0.59 % Model : x86_64 x86_64
% 0.09/0.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.59 % Memory : 8046.5625MB
% 0.09/0.59 % OS : Linux 6.8.0-71-generic
% 0.09/0.59 % CPULimit : 300
% 0.09/0.59 % WCLimit : 300
% 0.09/0.59 % DateTime : Mon Sep 28 03:06:35 UTC 2026
% 0.09/0.59 % CPUTime :
% 0.09/0.59 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.63 Running first-order model finding
% 0.13/0.63 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
% 0.13/0.68 % (3988974)Will run a generic schedule for satisfiability detection.
% 0.13/0.68 % (3988979)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1687014544_2999 on theBenchmark for (2999ds/0Mi)
% 0.13/0.68 % TRYING [1]
% 0.13/0.68 % TRYING [2]
% 0.13/0.68 % TRYING [3]
% 0.13/0.68 % TRYING [4]
% 0.13/0.68 % (3988980)% WARNING: option uhcvi not known.
% 0.13/0.68 % TRYING [5]
% 0.13/0.68 % (3988981)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2703684879:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.13/0.68 % (3988980)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4142983877:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.13/0.68 % (3988982)dis+10_1_sil=32000:sp=arity:random_seed=2586014193:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.13/0.68 % (3988983)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=944116332:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.13/0.68 % (3988984)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=188336179:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.13/0.68 % (3988985)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4185767204:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.13/0.68 % TRYING [6]
% 0.13/0.68 % (3988983) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3988974-3988983"...
% 0.13/0.68 % (3988982) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3988974-3988982"...
% 0.13/0.68 % (3988981) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3988974-3988981"...
% 0.13/0.68 % (3988985) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3988974-3988985"...
% 0.13/0.68 % (3988983)...printing done.
% 0.13/0.68 % (3988984) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3988974-3988984"...
% 0.13/0.68 % (3988982)...printing done.
% 0.13/0.68 % (3988981)...printing done.
% 0.13/0.68 % (3988985)...printing done.
% 0.13/0.68 % (3988980) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3988974-3988980"...
% 0.13/0.68 % (3988983)Refutation found. Thanks to Tanya!
% 0.13/0.68 % SZS status Theorem for theBenchmark
% 0.13/0.68 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.68 % (3988983)------------------------------
% 0.13/0.68 % (3988983)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.68 % (3988983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.68 % (3988983)CaDiCaL version: 2.1.3
% 0.13/0.68 % (3988983)Termination reason: Refutation
% 0.13/0.68 % (3988983)Time elapsed: 0.002 s
% 0.13/0.68 % (3988983)Peak memory usage: 12 MB
% 0.13/0.68 % (3988983)Instructions burned: 2 (million)
% 0.13/0.68 % (3988974)Success in time 0.039 s
% 0.13/0.68 % Vampire exiting
%------------------------------------------------------------------------------