%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ALG071+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 : 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 09:21:14 AM UTC 2026
% Result : Theorem 0.19s 0.34s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 61 ( 22 unt; 2 def)
% Number of atoms : 177 ( 60 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 186 ( 70 ~; 59 |; 33 &)
% ( 2 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 68 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( sorti1(X0)
=> ! [X1] :
( sorti1(X1)
=> sorti1(op1(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
fof(f3,axiom,
! [X0] :
( sorti1(X0)
=> ? [X1] :
( sorti1(X1)
& op1(X1,op1(X1,X0)) != X0
& op1(X0,op1(X1,X0)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(f4,axiom,
~ ! [X0] :
( sorti2(X0)
=> ? [X1] :
( sorti2(X1)
& op2(X1,op2(X1,X0)) != X0
& op2(X0,op2(X1,X0)) = X1 ) ),
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] :
( ! [X1] :
( sorti1(op1(X0,X1))
| ~ sorti1(X1) )
| ~ sorti1(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f9,plain,
! [X0] :
( ? [X1] :
( sorti1(X1)
& op1(X1,op1(X1,X0)) != X0
& op1(X0,op1(X1,X0)) = X1 )
| ~ sorti1(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f10,plain,
? [X0] :
( ! [X1] :
( ~ sorti2(X1)
| op2(X1,op2(X1,X0)) = X0
| op2(X0,op2(X1,X0)) != 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(f13,plain,
! [X0] :
( ( sorti1(sK0(X0))
& op1(sK0(X0),op1(sK0(X0),X0)) != X0
& sK0(X0) = op1(X0,op1(sK0(X0),X0)) )
| ~ sorti1(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f9]) ).
fof(f14,plain,
( ! [X1] :
( ~ sorti2(X1)
| sK1 = op2(X1,op2(X1,sK1))
| op2(sK1,op2(X1,sK1)) != X1 )
& 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(f16,plain,
! [X0,X1] :
( ~ sorti1(X1)
| sorti1(op1(X0,X1))
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f18,plain,
! [X0] :
( ~ sorti1(X0)
| sK0(X0) = op1(X0,op1(sK0(X0),X0)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f19,plain,
! [X0] :
( ~ sorti1(X0)
| op1(sK0(X0),op1(sK0(X0),X0)) != X0 ),
inference(cnf_transformation,[],[f13]) ).
fof(f20,plain,
! [X0] :
( ~ sorti1(X0)
| sorti1(sK0(X0)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f21,plain,
sorti2(sK1),
inference(cnf_transformation,[],[f14]) ).
fof(f22,plain,
! [X1] :
( ~ sorti2(X1)
| sK1 = op2(X1,op2(X1,sK1))
| op2(sK1,op2(X1,sK1)) != X1 ),
inference(cnf_transformation,[],[f14]) ).
fof(f23,plain,
! [X7] :
( ~ sorti2(X7)
| sorti1(j(X7)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f24,plain,
! [X6] :
( ~ sorti1(X6)
| sorti2(h(X6)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f25,plain,
! [X5] :
( ~ sorti1(X5)
| j(h(X5)) = X5 ),
inference(cnf_transformation,[],[f15]) ).
fof(f26,plain,
! [X4] :
( ~ sorti2(X4)
| h(j(X4)) = X4 ),
inference(cnf_transformation,[],[f15]) ).
fof(f28,plain,
! [X0,X1] :
( ~ sorti1(X1)
| h(op1(X0,X1)) = op2(h(X0),h(X1))
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f30,plain,
sK1 = h(j(sK1)),
inference(resolution,[],[f21,f26]) ).
fof(f31,plain,
sorti1(j(sK1)),
inference(resolution,[],[f21,f23]) ).
fof(f32,plain,
sorti1(sK0(j(sK1))),
inference(resolution,[],[f31,f20]) ).
fof(f33,plain,
! [X0] :
( h(op1(X0,j(sK1))) = op2(h(X0),h(j(sK1)))
| ~ sorti1(X0) ),
inference(resolution,[],[f31,f28]) ).
fof(f37,plain,
! [X0] :
( ~ sorti1(X0)
| h(op1(X0,j(sK1))) = op2(h(X0),sK1) ),
inference(forward_demodulation,[],[f33,f30]) ).
fof(f38,plain,
! [X0] :
( ~ sorti1(X0)
| sorti1(op1(X0,j(sK1))) ),
inference(resolution,[],[f16,f31]) ).
fof(f43,plain,
sorti2(h(sK0(j(sK1)))),
inference(resolution,[],[f32,f24]) ).
fof(f45,plain,
sK0(j(sK1)) = op1(j(sK1),op1(sK0(j(sK1)),j(sK1))),
inference(resolution,[],[f18,f31]) ).
fof(f53,plain,
j(sK1) != op1(sK0(j(sK1)),op1(sK0(j(sK1)),j(sK1))),
inference(resolution,[],[f19,f31]) ).
fof(f63,plain,
( sK1 = op2(h(sK0(j(sK1))),op2(h(sK0(j(sK1))),sK1))
| h(sK0(j(sK1))) != op2(sK1,op2(h(sK0(j(sK1))),sK1)) ),
inference(resolution,[],[f22,f43]) ).
fof(f65,definition,
( spl2_1
<=> h(sK0(j(sK1))) = op2(sK1,op2(h(sK0(j(sK1))),sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f67,plain,
( h(sK0(j(sK1))) != op2(sK1,op2(h(sK0(j(sK1))),sK1))
| spl2_1 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f69,definition,
( spl2_2
<=> sK1 = op2(h(sK0(j(sK1))),op2(h(sK0(j(sK1))),sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f71,plain,
( sK1 = op2(h(sK0(j(sK1))),op2(h(sK0(j(sK1))),sK1))
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f72,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f63,f69,f65]) ).
fof(f105,plain,
sorti1(op1(sK0(j(sK1)),j(sK1))),
inference(resolution,[],[f38,f32]) ).
fof(f117,plain,
op2(h(sK0(j(sK1))),sK1) = h(op1(sK0(j(sK1)),j(sK1))),
inference(resolution,[],[f37,f32]) ).
fof(f122,plain,
! [X0] :
( ~ sorti1(X0)
| sorti1(op1(X0,op1(sK0(j(sK1)),j(sK1)))) ),
inference(resolution,[],[f105,f16]) ).
fof(f128,plain,
! [X0] :
( h(op1(X0,op1(sK0(j(sK1)),j(sK1)))) = op2(h(X0),h(op1(sK0(j(sK1)),j(sK1))))
| ~ sorti1(X0) ),
inference(resolution,[],[f105,f28]) ).
fof(f132,plain,
! [X0] :
( ~ sorti1(X0)
| h(op1(X0,op1(sK0(j(sK1)),j(sK1)))) = op2(h(X0),op2(h(sK0(j(sK1))),sK1)) ),
inference(forward_demodulation,[],[f128,f117]) ).
fof(f760,plain,
sorti1(op1(sK0(j(sK1)),op1(sK0(j(sK1)),j(sK1)))),
inference(resolution,[],[f122,f32]) ).
fof(f1458,plain,
h(op1(j(sK1),op1(sK0(j(sK1)),j(sK1)))) = op2(h(j(sK1)),op2(h(sK0(j(sK1))),sK1)),
inference(resolution,[],[f132,f31]) ).
fof(f1461,plain,
op2(h(sK0(j(sK1))),op2(h(sK0(j(sK1))),sK1)) = h(op1(sK0(j(sK1)),op1(sK0(j(sK1)),j(sK1)))),
inference(resolution,[],[f132,f32]) ).
fof(f1514,plain,
op2(sK1,op2(h(sK0(j(sK1))),sK1)) = h(op1(j(sK1),op1(sK0(j(sK1)),j(sK1)))),
inference(forward_demodulation,[],[f1458,f30]) ).
fof(f1517,plain,
h(sK0(j(sK1))) = op2(sK1,op2(h(sK0(j(sK1))),sK1)),
inference(forward_demodulation,[],[f1514,f45]) ).
fof(f1518,plain,
( $false
| spl2_1 ),
inference(forward_subsumption_resolution,[],[f1517,f67]) ).
fof(f1519,plain,
spl2_1,
inference(avatar_contradiction_clause,[],[f1518]) ).
fof(f3125,plain,
op1(sK0(j(sK1)),op1(sK0(j(sK1)),j(sK1))) = j(h(op1(sK0(j(sK1)),op1(sK0(j(sK1)),j(sK1))))),
inference(resolution,[],[f760,f25]) ).
fof(f3146,plain,
op1(sK0(j(sK1)),op1(sK0(j(sK1)),j(sK1))) = j(op2(h(sK0(j(sK1))),op2(h(sK0(j(sK1))),sK1))),
inference(forward_demodulation,[],[f3125,f1461]) ).
fof(f3154,plain,
( j(sK1) = op1(sK0(j(sK1)),op1(sK0(j(sK1)),j(sK1)))
| ~ spl2_2 ),
inference(forward_demodulation,[],[f3146,f71]) ).
fof(f3158,plain,
( $false
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f3154,f53]) ).
fof(f3159,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f3158]) ).
cnf(s1,plain,
( ~ spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f72]) ).
cnf(s21,plain,
spl2_1,
inference(sat_conversion,[],[f1519]) ).
cnf(s44,plain,
~ spl2_2,
inference(sat_conversion,[],[f3159]) ).
cnf(s45,plain,
$false,
inference(rat,[],[s1,s44,s21]) ).
fof(f3160,plain,
$false,
inference(avatar_sat_refutation,[],[s45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG071+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n020.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 19:25:50 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.19/0.34 % (449984)Will run a generic schedule for satisfiability detection.
% 0.19/0.34 % (449992)dis+10_1_sil=32000:sp=arity:random_seed=3057494896:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.34 % (449990)% WARNING: option uhcvi not known.
% 0.19/0.34 % (449989)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3276930710_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.34 % (449990)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2834339535:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.34 % (449991)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=636026576:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.34 % (449993)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1833468696:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.34 % (449995)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1401455573:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.34 % (449994)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=345829127:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.34 % TRYING [1]
% 0.19/0.34 % TRYING [2]
% 0.19/0.34 % TRYING [3]
% 0.19/0.34 % TRYING [4]
% 0.19/0.34 % (449992)Instruction limit reached!
% 0.19/0.34 % (449992)------------------------------
% 0.19/0.34 % (449992)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.34 % (449992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.34 % (449992)CaDiCaL version: 2.1.3
% 0.19/0.34 % (449992)Termination reason: Instruction limit
% 0.19/0.34 % (449992)Termination phase: Saturation
% 0.19/0.34 % (449992)Time elapsed: 0.029 s
% 0.19/0.34 % (449992)Peak memory usage: 12 MB
% 0.19/0.34 % (449992)Instructions burned: 104 (million)
% 0.19/0.34 % (450003)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=734094509:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.34 % TRYING [1]
% 0.19/0.34 % TRYING [2]
% 0.19/0.34 % TRYING [3]
% 0.19/0.34 % TRYING [4]
% 0.19/0.34 % (449993)Instruction limit reached!
% 0.19/0.34 % (449993)------------------------------
% 0.19/0.34 % (449993)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.34 % (449993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.34 % (449993)CaDiCaL version: 2.1.3
% 0.19/0.34 % (449993)Termination reason: Instruction limit
% 0.19/0.34 % (449993)Termination phase: Saturation
% 0.19/0.34 % (449993)Time elapsed: 0.062 s
% 0.19/0.34 % (449993)Peak memory usage: 13 MB
% 0.19/0.34 % (449993)Instructions burned: 117 (million)
% 0.19/0.34 % (449994) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-449984-449994"...
% 0.19/0.34 % (449994)...printing done.
% 0.19/0.34 % (449994)Refutation found. Thanks to Tanya!
% 0.19/0.34 % SZS status Theorem for theBenchmark
% 0.19/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.34 % (449994)------------------------------
% 0.19/0.34 % (449994)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.34 % (449994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.34 % (449994)CaDiCaL version: 2.1.3
% 0.19/0.34 % (449994)Termination reason: Refutation
% 0.19/0.34 % (449994)Time elapsed: 0.067 s
% 0.19/0.34 % (449994)Peak memory usage: 14 MB
% 0.19/0.34 % (449994)Instructions burned: 122 (million)
% 0.19/0.34 % (449984)Success in time 0.108 s
% 0.19/0.34 % Vampire exiting
%------------------------------------------------------------------------------