%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ALG030+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 09:20:09 AM UTC 2026
% Result : Theorem 0.25s 0.36s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 35 ( 15 unt; 0 def)
% Number of atoms : 123 ( 44 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 134 ( 46 ~; 37 |; 27 &)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 61 ( 59 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
~ ! [X0] :
( sorti1(X0)
=> ! [X1] :
( sorti1(X1)
=> op1(X0,X1) = op1(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(f4,axiom,
~ ~ ! [X0] :
( sorti2(X0)
=> ! [X1] :
( sorti2(X1)
=> op2(X0,X1) = op2(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
fof(f5,conjecture,
( ( ! [X0] :
( sorti1(X0)
=> sorti2(h(X0)) )
& ! [X1] :
( sorti2(X1)
=> sorti1(j(X1)) ) )
=> ~ ( ! [X2] :
( sorti1(X2)
=> ! [X3] :
( sorti1(X3)
=> h(op1(X2,X3)) = op2(h(X2),h(X3)) ) )
& ! [X4] :
( sorti2(X4)
=> ! [X5] :
( sorti2(X5)
=> j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
& ! [X6] :
( sorti2(X6)
=> h(j(X6)) = X6 )
& ! [X7] :
( sorti1(X7)
=> j(h(X7)) = X7 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f6,negated_conjecture,
~ ( ( ! [X0] :
( sorti1(X0)
=> sorti2(h(X0)) )
& ! [X1] :
( sorti2(X1)
=> sorti1(j(X1)) ) )
=> ~ ( ! [X2] :
( sorti1(X2)
=> ! [X3] :
( sorti1(X3)
=> h(op1(X2,X3)) = op2(h(X2),h(X3)) ) )
& ! [X4] :
( sorti2(X4)
=> ! [X5] :
( sorti2(X5)
=> j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
& ! [X6] :
( sorti2(X6)
=> h(j(X6)) = X6 )
& ! [X7] :
( sorti1(X7)
=> j(h(X7)) = X7 ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,plain,
! [X0] :
( sorti2(X0)
=> ! [X1] :
( sorti2(X1)
=> op2(X0,X1) = op2(X1,X0) ) ),
inference(flattening,[],[f4]) ).
fof(f10,plain,
? [X0] :
( ? [X1] :
( op1(X0,X1) != op1(X1,X0)
& sorti1(X1) )
& sorti1(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f11,plain,
! [X0] :
( ! [X1] :
( op2(X0,X1) = op2(X1,X0)
| ~ sorti2(X1) )
| ~ sorti2(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f12,plain,
( ! [X2] :
( ! [X3] :
( h(op1(X2,X3)) = op2(h(X2),h(X3))
| ~ sorti1(X3) )
| ~ sorti1(X2) )
& ! [X4] :
( ! [X5] :
( j(op2(X4,X5)) = op1(j(X4),j(X5))
| ~ sorti2(X5) )
| ~ sorti2(X4) )
& ! [X6] :
( h(j(X6)) = X6
| ~ sorti2(X6) )
& ! [X7] :
( j(h(X7)) = X7
| ~ sorti1(X7) )
& ! [X0] :
( sorti2(h(X0))
| ~ sorti1(X0) )
& ! [X1] :
( sorti1(j(X1))
| ~ sorti2(X1) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f13,plain,
( ! [X2] :
( ! [X3] :
( h(op1(X2,X3)) = op2(h(X2),h(X3))
| ~ sorti1(X3) )
| ~ sorti1(X2) )
& ! [X4] :
( ! [X5] :
( j(op2(X4,X5)) = op1(j(X4),j(X5))
| ~ sorti2(X5) )
| ~ sorti2(X4) )
& ! [X6] :
( h(j(X6)) = X6
| ~ sorti2(X6) )
& ! [X7] :
( j(h(X7)) = X7
| ~ sorti1(X7) )
& ! [X0] :
( sorti2(h(X0))
| ~ sorti1(X0) )
& ! [X1] :
( sorti1(j(X1))
| ~ sorti2(X1) ) ),
inference(flattening,[],[f12]) ).
fof(f14,plain,
( op1(sK0,sK1) != op1(sK1,sK0)
& sorti1(sK1)
& sorti1(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f10]) ).
fof(f15,plain,
( ! [X0] :
( ! [X1] :
( h(op1(X0,X1)) = op2(h(X0),h(X1))
| ~ sorti1(X1) )
| ~ sorti1(X0) )
& ! [X2] :
( ! [X3] :
( j(op2(X2,X3)) = op1(j(X2),j(X3))
| ~ sorti2(X3) )
| ~ sorti2(X2) )
& ! [X4] :
( h(j(X4)) = X4
| ~ sorti2(X4) )
& ! [X5] :
( j(h(X5)) = X5
| ~ sorti1(X5) )
& ! [X6] :
( sorti2(h(X6))
| ~ sorti1(X6) )
& ! [X7] :
( sorti1(j(X7))
| ~ sorti2(X7) ) ),
inference(rectify,[],[f13]) ).
fof(f18,plain,
sorti1(sK0),
inference(cnf_transformation,[],[f14]) ).
fof(f19,plain,
sorti1(sK1),
inference(cnf_transformation,[],[f14]) ).
fof(f20,plain,
op1(sK0,sK1) != op1(sK1,sK0),
inference(cnf_transformation,[],[f14]) ).
fof(f21,plain,
! [X0,X1] :
( ~ sorti2(X1)
| op2(X0,X1) = op2(X1,X0)
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f11]) ).
fof(f23,plain,
! [X6] :
( ~ sorti1(X6)
| sorti2(h(X6)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f24,plain,
! [X5] :
( ~ sorti1(X5)
| j(h(X5)) = X5 ),
inference(cnf_transformation,[],[f15]) ).
fof(f26,plain,
! [X2,X3] :
( ~ sorti2(X3)
| j(op2(X2,X3)) = op1(j(X2),j(X3))
| ~ sorti2(X2) ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
sK0 = j(h(sK0)),
inference(resolution,[],[f18,f24]) ).
fof(f30,plain,
sorti2(h(sK0)),
inference(resolution,[],[f18,f23]) ).
fof(f32,plain,
sK1 = j(h(sK1)),
inference(resolution,[],[f19,f24]) ).
fof(f33,plain,
sorti2(h(sK1)),
inference(resolution,[],[f19,f23]) ).
fof(f34,plain,
! [X0] :
( j(op2(X0,h(sK0))) = op1(j(X0),j(h(sK0)))
| ~ sorti2(X0) ),
inference(resolution,[],[f30,f26]) ).
fof(f38,plain,
! [X0] :
( ~ sorti2(X0)
| j(op2(X0,h(sK0))) = op1(j(X0),sK0) ),
inference(forward_demodulation,[],[f34,f29]) ).
fof(f39,plain,
! [X0] :
( j(op2(X0,h(sK1))) = op1(j(X0),j(h(sK1)))
| ~ sorti2(X0) ),
inference(resolution,[],[f33,f26]) ).
fof(f43,plain,
! [X0] :
( ~ sorti2(X0)
| j(op2(X0,h(sK1))) = op1(j(X0),sK1) ),
inference(forward_demodulation,[],[f39,f32]) ).
fof(f48,plain,
! [X0] :
( ~ sorti2(X0)
| op2(X0,h(sK0)) = op2(h(sK0),X0) ),
inference(resolution,[],[f21,f30]) ).
fof(f127,plain,
op2(h(sK1),h(sK0)) = op2(h(sK0),h(sK1)),
inference(resolution,[],[f48,f33]) ).
fof(f172,plain,
j(op2(h(sK1),h(sK0))) = op1(j(h(sK1)),sK0),
inference(resolution,[],[f38,f33]) ).
fof(f183,plain,
op1(sK1,sK0) = j(op2(h(sK1),h(sK0))),
inference(forward_demodulation,[],[f172,f32]) ).
fof(f187,plain,
op1(sK1,sK0) = j(op2(h(sK0),h(sK1))),
inference(forward_demodulation,[],[f183,f127]) ).
fof(f230,plain,
j(op2(h(sK0),h(sK1))) = op1(j(h(sK0)),sK1),
inference(resolution,[],[f43,f30]) ).
fof(f245,plain,
op1(sK0,sK1) = j(op2(h(sK0),h(sK1))),
inference(forward_demodulation,[],[f230,f29]) ).
fof(f525,plain,
op1(sK0,sK1) = op1(sK1,sK0),
inference(superposition,[],[f187,f245]) ).
fof(f527,plain,
$false,
inference(forward_subsumption_resolution,[],[f525,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ALG030+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.26 % Computer : n019.cluster.edu
% 0.10/0.26 % Model : x86_64 x86_64
% 0.10/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.26 % Memory : 8046.5625MB
% 0.10/0.26 % OS : Linux 6.8.0-71-generic
% 0.10/0.26 % CPULimit : 300
% 0.10/0.26 % WCLimit : 300
% 0.10/0.26 % DateTime : Mon Sep 28 19:19:33 UTC 2026
% 0.10/0.26 % CPUTime :
% 0.10/0.26 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.25/0.31 Running first-order model finding
% 0.25/0.31 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
% 0.25/0.36 % (137316)Will run a generic schedule for satisfiability detection.
% 0.25/0.36 % (137326)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2812017380:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.25/0.36 % (137325)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1282557371:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.25/0.36 % (137322)% WARNING: option uhcvi not known.
% 0.25/0.36 % (137326) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-137316-137326"...
% 0.25/0.36 % (137326)...printing done.
% 0.25/0.36 % (137321)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3920452650_3000 on theBenchmark for (3000ds/0Mi)
% 0.25/0.36 % (137322)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2160599700:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.25/0.36 % (137323)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1204534555:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.25/0.36 % (137326)Refutation found. Thanks to Tanya!
% 0.25/0.36 % SZS status Theorem for theBenchmark
% 0.25/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.36 % (137326)------------------------------
% 0.25/0.36 % (137326)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.36 % (137326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.36 % (137326)CaDiCaL version: 2.1.3
% 0.25/0.36 % (137326)Termination reason: Refutation
% 0.25/0.36 % (137326)Time elapsed: 0.010 s
% 0.25/0.36 % (137326)Peak memory usage: 11 MB
% 0.25/0.36 % (137326)Instructions burned: 17 (million)
% 0.25/0.36 % (137316)Success in time 0.034 s
% 0.25/0.36 % Vampire exiting
%------------------------------------------------------------------------------