%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ALG073+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 0.08s 0.26s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 69 ( 21 unt; 4 def)
% Number of atoms : 200 ( 60 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 219 ( 88 ~; 79 |; 26 &)
% ( 4 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 58 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( sorti1(X0)
=> ! [X1] :
( sorti1(X1)
=> sorti1(op1(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
fof(f2,axiom,
! [X0] :
( sorti2(X0)
=> ! [X1] :
( sorti2(X1)
=> sorti2(op2(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
fof(f3,axiom,
? [X0] :
( sorti1(X0)
& ? [X1] :
( sorti1(X1)
& op1(X0,X0) = X1
& op1(X1,X1) = X0
& op1(X0,X1) != X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(f4,axiom,
~ ? [X0] :
( sorti2(X0)
& ? [X1] :
( sorti2(X1)
& op2(X0,X0) = X1
& op2(X1,X1) = X0
& op2(X0,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] :
( ! [X1] :
( sorti1(op1(X0,X1))
| ~ sorti1(X1) )
| ~ sorti1(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f8,plain,
! [X0] :
( ! [X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1) )
| ~ sorti2(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f9,plain,
! [X0] :
( ~ sorti2(X0)
| ! [X1] :
( ~ sorti2(X1)
| op2(X0,X0) != X1
| op2(X1,X1) != X0
| op2(X0,X1) = X0 ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f10,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(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(flattening,[],[f10]) ).
fof(f12,plain,
! [X0,X1] :
( sorti1(op1(X0,X1))
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
! [X0,X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f8]) ).
fof(f14,plain,
sK0 != op1(sK0,sK1),
inference(cnf_transformation,[],[f3]) ).
fof(f15,plain,
sK0 = op1(sK1,sK1),
inference(cnf_transformation,[],[f3]) ).
fof(f16,plain,
sK1 = op1(sK0,sK0),
inference(cnf_transformation,[],[f3]) ).
fof(f17,plain,
sorti1(sK1),
inference(cnf_transformation,[],[f3]) ).
fof(f18,plain,
sorti1(sK0),
inference(cnf_transformation,[],[f3]) ).
fof(f19,plain,
! [X0,X1] :
( op2(X0,X1) = X0
| op2(X1,X1) != X0
| op2(X0,X0) != X1
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f9]) ).
fof(f20,plain,
! [X2,X3] :
( ~ sorti1(X2)
| ~ sorti1(X3)
| h(op1(X2,X3)) = op2(h(X2),h(X3)) ),
inference(cnf_transformation,[],[f11]) ).
fof(f23,plain,
! [X7] :
( ~ sorti1(X7)
| j(h(X7)) = X7 ),
inference(cnf_transformation,[],[f11]) ).
fof(f24,plain,
! [X0] :
( sorti2(h(X0))
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f11]) ).
fof(f26,plain,
! [X1] :
( ~ sorti2(op2(X1,X1))
| op2(op2(X1,X1),op2(X1,X1)) != X1
| ~ sorti2(X1)
| op2(X1,X1) = op2(op2(X1,X1),X1) ),
inference(equality_resolution,[],[f19]) ).
fof(f38,plain,
! [X0] :
( ~ sorti1(X0)
| h(op1(X0,sK1)) = op2(h(X0),h(sK1)) ),
inference(resolution,[],[f17,f20]) ).
fof(f45,plain,
! [X0] :
( ~ sorti1(X0)
| h(op1(X0,sK0)) = op2(h(X0),h(sK0)) ),
inference(resolution,[],[f18,f20]) ).
fof(f47,plain,
sK0 = j(h(sK0)),
inference(resolution,[],[f18,f23]) ).
fof(f51,plain,
h(op1(sK1,sK1)) = op2(h(sK1),h(sK1)),
inference(resolution,[],[f38,f17]) ).
fof(f52,plain,
h(op1(sK0,sK1)) = op2(h(sK0),h(sK1)),
inference(resolution,[],[f38,f18]) ).
fof(f53,plain,
h(sK0) = op2(h(sK1),h(sK1)),
inference(forward_demodulation,[],[f51,f15]) ).
fof(f59,plain,
! [X0,X1] :
( ~ sorti1(X0)
| ~ sorti1(X1)
| op1(X1,X0) = j(h(op1(X1,X0))) ),
inference(resolution,[],[f12,f23]) ).
fof(f73,plain,
( sorti2(h(sK0))
| ~ sorti2(h(sK1))
| ~ sorti2(h(sK1)) ),
inference(superposition,[],[f13,f53]) ).
fof(f75,plain,
( sorti2(h(sK0))
| ~ sorti2(h(sK1)) ),
inference(duplicate_literal_removal,[],[f73]) ).
fof(f77,definition,
( spl2_1
<=> sorti2(h(sK0)) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f78,plain,
( sorti2(h(sK0))
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f81,definition,
( spl2_2
<=> sorti2(h(sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f82,plain,
( sorti2(h(sK1))
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f83,plain,
( ~ sorti2(h(sK1))
| spl2_2 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f89,plain,
( ~ spl2_2
| spl2_1 ),
inference(avatar_split_clause,[],[f75,f77,f81]) ).
fof(f90,plain,
( ~ sorti1(sK1)
| spl2_2 ),
inference(resolution,[],[f83,f24]) ).
fof(f91,plain,
( $false
| spl2_2 ),
inference(forward_subsumption_resolution,[],[f90,f17]) ).
fof(f92,plain,
spl2_2,
inference(avatar_contradiction_clause,[],[f91]) ).
fof(f94,plain,
( ~ sorti2(h(sK0))
| h(sK1) != op2(h(sK0),h(sK0))
| ~ sorti2(h(sK1))
| h(sK0) = op2(h(sK0),h(sK1)) ),
inference(superposition,[],[f26,f53]) ).
fof(f96,plain,
( h(sK1) != op2(h(sK0),h(sK0))
| ~ sorti2(h(sK1))
| h(sK0) = op2(h(sK0),h(sK1))
| ~ spl2_1 ),
inference(forward_subsumption_resolution,[],[f94,f78]) ).
fof(f97,plain,
( h(sK1) != op2(h(sK0),h(sK0))
| h(sK0) = op2(h(sK0),h(sK1))
| ~ spl2_1
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f96,f82]) ).
fof(f98,plain,
( h(sK0) = h(op1(sK0,sK1))
| h(sK1) != op2(h(sK0),h(sK0))
| ~ spl2_1
| ~ spl2_2 ),
inference(forward_demodulation,[],[f97,f52]) ).
fof(f100,definition,
( spl2_4
<=> h(sK1) = op2(h(sK0),h(sK0)) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f102,plain,
( h(sK1) != op2(h(sK0),h(sK0))
| spl2_4 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f104,definition,
( spl2_5
<=> h(sK0) = h(op1(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
fof(f106,plain,
( h(sK0) = h(op1(sK0,sK1))
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f107,plain,
( ~ spl2_4
| spl2_5
| ~ spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f98,f81,f77,f104,f100]) ).
fof(f132,plain,
op2(h(sK0),h(sK0)) = h(op1(sK0,sK0)),
inference(resolution,[],[f45,f18]) ).
fof(f134,plain,
h(sK1) = op2(h(sK0),h(sK0)),
inference(forward_demodulation,[],[f132,f16]) ).
fof(f135,plain,
( $false
| spl2_4 ),
inference(forward_subsumption_resolution,[],[f134,f102]) ).
fof(f136,plain,
spl2_4,
inference(avatar_contradiction_clause,[],[f135]) ).
fof(f164,plain,
! [X0] :
( ~ sorti1(X0)
| op1(X0,sK1) = j(h(op1(X0,sK1))) ),
inference(resolution,[],[f59,f17]) ).
fof(f493,plain,
op1(sK0,sK1) = j(h(op1(sK0,sK1))),
inference(resolution,[],[f164,f18]) ).
fof(f496,plain,
( op1(sK0,sK1) = j(h(sK0))
| ~ spl2_5 ),
inference(forward_demodulation,[],[f493,f106]) ).
fof(f498,plain,
( sK0 = op1(sK0,sK1)
| ~ spl2_5 ),
inference(forward_demodulation,[],[f496,f47]) ).
fof(f500,plain,
( $false
| ~ spl2_5 ),
inference(forward_subsumption_resolution,[],[f498,f14]) ).
fof(f501,plain,
~ spl2_5,
inference(avatar_contradiction_clause,[],[f500]) ).
cnf(s2,plain,
( spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f89]) ).
cnf(s3,plain,
spl2_2,
inference(sat_conversion,[],[f92]) ).
cnf(s4,plain,
( ~ spl2_1
| ~ spl2_2
| ~ spl2_4
| spl2_5 ),
inference(sat_conversion,[],[f107]) ).
cnf(s5,plain,
spl2_4,
inference(sat_conversion,[],[f136]) ).
cnf(s6,plain,
~ spl2_5,
inference(sat_conversion,[],[f501]) ).
cnf(s7,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(rat,[],[s4,s6,s5]) ).
cnf(s8,plain,
~ spl2_1,
inference(rat,[],[s7,s3]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s2,s3,s8]) ).
fof(f503,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG073+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n020.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 19:25:34 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 0.08/0.26 % (449571)Will run a generic schedule for satisfiability detection.
% 0.08/0.26 % (449580)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3593631823:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.26 % (449577)% WARNING: option uhcvi not known.
% 0.08/0.26 % (449576)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2828919168_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.26 % (449577)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3350188800:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.26 % (449580) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-449571-449580"...
% 0.08/0.26 % (449578)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=375747570:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.26 % (449579)dis+10_1_sil=32000:sp=arity:random_seed=1090435700:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.26 % (449582)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2435247512:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.26 % (449581)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3526766232:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.26 % (449580)...printing done.
% 0.08/0.26 % TRYING [1]
% 0.08/0.26 % TRYING [2]
% 0.08/0.26 % TRYING [3]
% 0.08/0.26 % (449580)Refutation found. Thanks to Tanya!
% 0.08/0.26 % SZS status Theorem for theBenchmark
% 0.08/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.26 % (449580)------------------------------
% 0.08/0.26 % (449580)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (449580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (449580)CaDiCaL version: 2.1.3
% 0.08/0.26 % (449580)Termination reason: Refutation
% 0.08/0.26 % (449580)Time elapsed: 0.008 s
% 0.08/0.26 % (449580)Peak memory usage: 12 MB
% 0.08/0.26 % (449580)Instructions burned: 22 (million)
% 0.08/0.26 % (449571)Success in time 0.033 s
% 0.08/0.26 % Vampire exiting
%------------------------------------------------------------------------------