%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ALG069+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 : n006.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 09:21:14 AM UTC 2026
% Result : Theorem 0.10s 0.26s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 30 ( 11 unt; 0 def)
% Number of atoms : 116 ( 37 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 131 ( 45 ~; 37 |; 29 &)
% ( 0 <=>; 20 =>; 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; 1 con; 0-2 aty)
% Number of variables : 59 ( 55 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( sorti1(X0)
=> ? [X1] :
( sorti1(X1)
& op1(X1,X1) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(f4,axiom,
~ ! [X0] :
( sorti2(X0)
=> ? [X1] :
( sorti2(X1)
& op2(X1,X1) = X0 ) ),
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(f9,plain,
! [X0] :
( ? [X1] :
( sorti1(X1)
& op1(X1,X1) = X0 )
| ~ sorti1(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f10,plain,
? [X0] :
( ! [X1] :
( ~ sorti2(X1)
| op2(X1,X1) != X0 )
& 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(f13,plain,
! [X0] :
( ( sorti1(sK0(X0))
& op1(sK0(X0),sK0(X0)) = X0 )
| ~ sorti1(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f9]) ).
fof(f14,plain,
( ! [X1] :
( ~ sorti2(X1)
| op2(X1,X1) != sK1 )
& sorti2(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,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,[],[f12]) ).
fof(f18,plain,
! [X0] :
( ~ sorti1(X0)
| op1(sK0(X0),sK0(X0)) = X0 ),
inference(cnf_transformation,[],[f13]) ).
fof(f19,plain,
! [X0] :
( ~ sorti1(X0)
| sorti1(sK0(X0)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f20,plain,
sorti2(sK1),
inference(cnf_transformation,[],[f14]) ).
fof(f21,plain,
! [X1] :
( ~ sorti2(X1)
| op2(X1,X1) != sK1 ),
inference(cnf_transformation,[],[f14]) ).
fof(f22,plain,
! [X7] :
( ~ sorti2(X7)
| sorti1(j(X7)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f23,plain,
! [X6] :
( ~ sorti1(X6)
| sorti2(h(X6)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f25,plain,
! [X4] :
( ~ sorti2(X4)
| h(j(X4)) = X4 ),
inference(cnf_transformation,[],[f15]) ).
fof(f27,plain,
! [X0,X1] :
( ~ sorti1(X1)
| h(op1(X0,X1)) = op2(h(X0),h(X1))
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
sK1 = h(j(sK1)),
inference(resolution,[],[f20,f25]) ).
fof(f30,plain,
sorti1(j(sK1)),
inference(resolution,[],[f20,f22]) ).
fof(f31,plain,
sorti1(sK0(j(sK1))),
inference(resolution,[],[f30,f19]) ).
fof(f39,plain,
! [X0] :
( ~ sorti1(X0)
| h(op1(X0,sK0(j(sK1)))) = op2(h(X0),h(sK0(j(sK1)))) ),
inference(resolution,[],[f31,f27]) ).
fof(f41,plain,
sorti2(h(sK0(j(sK1)))),
inference(resolution,[],[f31,f23]) ).
fof(f50,plain,
j(sK1) = op1(sK0(j(sK1)),sK0(j(sK1))),
inference(resolution,[],[f18,f30]) ).
fof(f54,plain,
sK1 != op2(h(sK0(j(sK1))),h(sK0(j(sK1)))),
inference(resolution,[],[f41,f21]) ).
fof(f211,plain,
op2(h(sK0(j(sK1))),h(sK0(j(sK1)))) = h(op1(sK0(j(sK1)),sK0(j(sK1)))),
inference(resolution,[],[f39,f31]) ).
fof(f224,plain,
h(j(sK1)) = op2(h(sK0(j(sK1))),h(sK0(j(sK1)))),
inference(forward_demodulation,[],[f211,f50]) ).
fof(f226,plain,
sK1 = op2(h(sK0(j(sK1))),h(sK0(j(sK1)))),
inference(forward_demodulation,[],[f224,f29]) ).
fof(f227,plain,
$false,
inference(forward_subsumption_resolution,[],[f226,f54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG069+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.18 % Computer : n006.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Mon Sep 28 19:24:40 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.21 Running first-order model finding
% 0.10/0.21 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
% 0.10/0.26 % (91590)Will run a generic schedule for satisfiability detection.
% 0.10/0.26 % (91599)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2228994654:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.26 % (91596)% WARNING: option uhcvi not known.
% 0.10/0.26 % (91595)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=443716508_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.26 % (91597)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2557849557:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.26 % (91598)dis+10_1_sil=32000:sp=arity:random_seed=2404875645:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.26 % (91596)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1726981568:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.26 % (91600)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2342422226:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.26 % (91601)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3855745133:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.26 % TRYING [1]
% 0.10/0.26 % TRYING [2]
% 0.10/0.26 % TRYING [3]
% 0.10/0.26 % TRYING [4]
% 0.10/0.26 % (91600) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-91590-91600"...
% 0.10/0.26 % (91600)...printing done.
% 0.10/0.26 % TRYING [5]
% 0.10/0.26 % (91600)Refutation found. Thanks to Tanya!
% 0.10/0.26 % SZS status Theorem for theBenchmark
% 0.10/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.26 % (91600)------------------------------
% 0.10/0.26 % (91600)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.26 % (91600)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.26 % (91600)CaDiCaL version: 2.1.3
% 0.10/0.26 % (91600)Termination reason: Refutation
% 0.10/0.26 % (91600)Time elapsed: 0.006 s
% 0.10/0.26 % (91600)Peak memory usage: 11 MB
% 0.10/0.26 % (91600)Instructions burned: 9 (million)
% 0.10/0.26 % (91590)Success in time 0.038 s
% 0.10/0.26 % Vampire exiting
%------------------------------------------------------------------------------