%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ALG178+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 09:28:49 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 41 ( 17 unt; 0 def)
% Number of atoms : 125 ( 41 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 130 ( 46 ~; 40 |; 20 &)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 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 : 64 ( 62 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( sorti2(X0)
=> ! [X1] :
( sorti2(X1)
=> sorti2(op2(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
fof(f3,axiom,
! [X0] :
( sorti1(X0)
=> ! [X1] :
( sorti1(X1)
=> op1(X0,op1(X0,X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(f4,axiom,
~ ! [X0] :
( sorti2(X0)
=> ! [X1] :
( sorti2(X1)
=> op2(X0,op2(X0,X1)) = X1 ) ),
file('/export/starexec/sandbox2/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/sandbox2/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(f8,plain,
! [X0] :
( ! [X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1) )
| ~ sorti2(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f9,plain,
! [X0] :
( ! [X1] :
( op1(X0,op1(X0,X1)) = X1
| ~ sorti1(X1) )
| ~ sorti1(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f10,plain,
? [X0] :
( ? [X1] :
( op2(X0,op2(X0,X1)) != X1
& sorti2(X1) )
& sorti2(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f11,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(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(flattening,[],[f11]) ).
fof(f14,plain,
! [X0,X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f8]) ).
fof(f15,plain,
! [X0,X1] :
( ~ sorti1(X0)
| ~ sorti1(X1)
| op1(X0,op1(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f16,plain,
sorti2(sK1),
inference(cnf_transformation,[],[f10]) ).
fof(f17,plain,
sK1 != op2(sK0,op2(sK0,sK1)),
inference(cnf_transformation,[],[f10]) ).
fof(f18,plain,
sorti2(sK0),
inference(cnf_transformation,[],[f10]) ).
fof(f19,plain,
! [X2,X3] :
( ~ sorti1(X2)
| ~ sorti1(X3)
| h(op1(X2,X3)) = op2(h(X2),h(X3)) ),
inference(cnf_transformation,[],[f12]) ).
fof(f20,plain,
! [X4,X5] :
( ~ sorti2(X4)
| ~ sorti2(X5)
| j(op2(X4,X5)) = op1(j(X4),j(X5)) ),
inference(cnf_transformation,[],[f12]) ).
fof(f21,plain,
! [X6] :
( ~ sorti2(X6)
| h(j(X6)) = X6 ),
inference(cnf_transformation,[],[f12]) ).
fof(f24,plain,
! [X1] :
( ~ sorti2(X1)
| sorti1(j(X1)) ),
inference(cnf_transformation,[],[f12]) ).
fof(f34,plain,
! [X0] :
( ~ sorti2(X0)
| j(op2(X0,sK1)) = op1(j(X0),j(sK1)) ),
inference(resolution,[],[f16,f20]) ).
fof(f36,plain,
sK1 = h(j(sK1)),
inference(resolution,[],[f16,f21]) ).
fof(f37,plain,
sorti1(j(sK1)),
inference(resolution,[],[f16,f24]) ).
fof(f49,plain,
sK0 = h(j(sK0)),
inference(resolution,[],[f18,f21]) ).
fof(f50,plain,
sorti1(j(sK0)),
inference(resolution,[],[f18,f24]) ).
fof(f54,plain,
! [X0] :
( ~ sorti1(X0)
| h(op1(j(sK0),X0)) = op2(h(j(sK0)),h(X0)) ),
inference(resolution,[],[f50,f19]) ).
fof(f56,plain,
! [X0] :
( ~ sorti1(X0)
| h(op1(j(sK0),X0)) = op2(sK0,h(X0)) ),
inference(forward_demodulation,[],[f54,f49]) ).
fof(f71,plain,
! [X0,X1] :
( ~ sorti2(X0)
| ~ sorti2(X1)
| op2(X1,X0) = h(j(op2(X1,X0))) ),
inference(resolution,[],[f14,f21]) ).
fof(f72,plain,
! [X0,X1] :
( ~ sorti2(X0)
| ~ sorti2(X1)
| sorti1(j(op2(X1,X0))) ),
inference(resolution,[],[f14,f24]) ).
fof(f76,plain,
! [X0] :
( ~ sorti2(X0)
| sorti1(j(op2(X0,sK1))) ),
inference(resolution,[],[f72,f16]) ).
fof(f83,plain,
! [X0] :
( ~ sorti1(X0)
| op1(j(sK0),op1(j(sK0),X0)) = X0 ),
inference(resolution,[],[f15,f50]) ).
fof(f95,plain,
j(op2(sK0,sK1)) = op1(j(sK0),j(sK1)),
inference(resolution,[],[f34,f18]) ).
fof(f121,plain,
sorti1(j(op2(sK0,sK1))),
inference(resolution,[],[f76,f18]) ).
fof(f160,plain,
! [X0] :
( ~ sorti2(X0)
| op2(X0,sK1) = h(j(op2(X0,sK1))) ),
inference(resolution,[],[f71,f16]) ).
fof(f435,plain,
j(sK1) = op1(j(sK0),op1(j(sK0),j(sK1))),
inference(resolution,[],[f83,f37]) ).
fof(f437,plain,
j(sK1) = op1(j(sK0),j(op2(sK0,sK1))),
inference(forward_demodulation,[],[f435,f95]) ).
fof(f487,plain,
op2(sK0,sK1) = h(j(op2(sK0,sK1))),
inference(resolution,[],[f160,f18]) ).
fof(f759,plain,
h(op1(j(sK0),j(op2(sK0,sK1)))) = op2(sK0,h(j(op2(sK0,sK1)))),
inference(resolution,[],[f56,f121]) ).
fof(f768,plain,
op2(sK0,op2(sK0,sK1)) = h(op1(j(sK0),j(op2(sK0,sK1)))),
inference(forward_demodulation,[],[f759,f487]) ).
fof(f777,plain,
op2(sK0,op2(sK0,sK1)) = h(j(sK1)),
inference(forward_demodulation,[],[f768,f437]) ).
fof(f780,plain,
sK1 = op2(sK0,op2(sK0,sK1)),
inference(forward_demodulation,[],[f777,f36]) ).
fof(f783,plain,
$false,
inference(forward_subsumption_resolution,[],[f780,f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG178+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n003.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 19:41:43 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.29 % (1902474)Will run a generic schedule for satisfiability detection.
% 0.20/0.29 % (1902479)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2365063937_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.29 % TRYING [1]
% 0.20/0.29 % TRYING [2]
% 0.20/0.29 % TRYING [3]
% 0.20/0.29 % TRYING [4]
% 0.20/0.29 % (1902480)% WARNING: option uhcvi not known.
% 0.20/0.29 % (1902480)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3000969152:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.29 % (1902481)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=50323019:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.29 % (1902482)dis+10_1_sil=32000:sp=arity:random_seed=2463202745:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.29 % (1902483)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1369986515:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.29 % (1902485)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4232563657:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.29 % (1902484)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2640959162:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.29 % TRYING [5]
% 0.20/0.29 % TRYING [6]
% 0.20/0.29 % (1902483) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1902474-1902483"...
% 0.20/0.29 % (1902482) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1902474-1902482"...
% 0.20/0.29 % (1902483)...printing done.
% 0.20/0.29 % (1902483)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.29 % (1902483)------------------------------
% 0.20/0.29 % (1902483)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1902483)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1902483)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1902483)Termination reason: Refutation
% 0.20/0.29 % (1902483)Time elapsed: 0.024 s
% 0.20/0.29 % (1902483)Peak memory usage: 12 MB
% 0.20/0.29 % (1902483)Instructions burned: 41 (million)
% 0.20/0.29 % (1902474)Success in time 0.063 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------