%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ALG203+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 : 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 09:29:45 AM UTC 2026
% Result : Theorem 0.09s 0.27s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 54 ( 18 unt; 2 def)
% Number of atoms : 169 ( 53 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 189 ( 74 ~; 61 |; 32 &)
% ( 2 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 64 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
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)
& op1(X0,X0) = X0 )
& ? [X1] :
( sorti1(X1)
& op1(X1,X1) != X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(f4,axiom,
~ ( ? [X0] :
( sorti2(X0)
& op2(X0,X0) = X0 )
& ? [X1] :
( sorti2(X1)
& op2(X1,X1) != 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(f8,plain,
! [X0] :
( ! [X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1) )
| ~ sorti2(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f9,plain,
( ! [X0] :
( ~ sorti2(X0)
| op2(X0,X0) != X0 )
| ! [X1] :
( ~ sorti2(X1)
| op2(X1,X1) = X1 ) ),
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,
( sorti1(sK0)
& sK0 = op1(sK0,sK0)
& sorti1(sK1)
& sK1 != op1(sK1,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f3]) ).
fof(f13,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,[],[f11]) ).
fof(f15,plain,
! [X0,X1] :
( ~ sorti2(X1)
| sorti2(op2(X0,X1))
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f8]) ).
fof(f16,plain,
sK1 != op1(sK1,sK1),
inference(cnf_transformation,[],[f12]) ).
fof(f17,plain,
sorti1(sK1),
inference(cnf_transformation,[],[f12]) ).
fof(f18,plain,
sK0 = op1(sK0,sK0),
inference(cnf_transformation,[],[f12]) ).
fof(f19,plain,
sorti1(sK0),
inference(cnf_transformation,[],[f12]) ).
fof(f20,plain,
! [X0,X1] :
( ~ sorti2(X0)
| op2(X0,X0) != X0
| ~ sorti2(X1)
| op2(X1,X1) = X1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f22,plain,
! [X6] :
( ~ sorti1(X6)
| sorti2(h(X6)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f23,plain,
! [X5] :
( ~ sorti1(X5)
| j(h(X5)) = X5 ),
inference(cnf_transformation,[],[f13]) ).
fof(f25,plain,
! [X2,X3] :
( ~ sorti2(X3)
| j(op2(X2,X3)) = op1(j(X2),j(X3))
| ~ sorti2(X2) ),
inference(cnf_transformation,[],[f13]) ).
fof(f26,plain,
! [X0,X1] :
( ~ sorti1(X1)
| h(op1(X0,X1)) = op2(h(X0),h(X1))
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f28,definition,
( spl2_1
<=> ! [X1] :
( ~ sorti2(X1)
| op2(X1,X1) = X1 ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f29,plain,
( ! [X1] :
( ~ sorti2(X1)
| op2(X1,X1) = X1 )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f28]) ).
fof(f31,definition,
( spl2_2
<=> ! [X0] :
( ~ sorti2(X0)
| op2(X0,X0) != X0 ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f32,plain,
( ! [X0] :
( ~ sorti2(X0)
| op2(X0,X0) != X0 )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f31]) ).
fof(f33,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f20,f31,f28]) ).
fof(f35,plain,
sK1 = j(h(sK1)),
inference(resolution,[],[f17,f23]) ).
fof(f36,plain,
sorti2(h(sK1)),
inference(resolution,[],[f17,f22]) ).
fof(f37,plain,
! [X0] :
( ~ sorti1(X0)
| h(op1(X0,sK0)) = op2(h(X0),h(sK0)) ),
inference(resolution,[],[f19,f26]) ).
fof(f39,plain,
sorti2(h(sK0)),
inference(resolution,[],[f19,f22]) ).
fof(f40,plain,
! [X0] :
( j(op2(X0,h(sK1))) = op1(j(X0),j(h(sK1)))
| ~ sorti2(X0) ),
inference(resolution,[],[f36,f25]) ).
fof(f44,plain,
! [X0] :
( ~ sorti2(X0)
| j(op2(X0,h(sK1))) = op1(j(X0),sK1) ),
inference(forward_demodulation,[],[f40,f35]) ).
fof(f51,plain,
( h(sK0) != op2(h(sK0),h(sK0))
| ~ spl2_2 ),
inference(resolution,[],[f32,f39]) ).
fof(f54,plain,
! [X0] :
( ~ sorti2(X0)
| sorti2(op2(X0,h(sK1))) ),
inference(resolution,[],[f15,f36]) ).
fof(f56,plain,
sorti2(op2(h(sK1),h(sK1))),
inference(resolution,[],[f54,f36]) ).
fof(f60,plain,
sorti2(op2(op2(h(sK1),h(sK1)),h(sK1))),
inference(resolution,[],[f56,f54]) ).
fof(f67,plain,
op2(h(sK0),h(sK0)) = h(op1(sK0,sK0)),
inference(resolution,[],[f37,f19]) ).
fof(f68,plain,
h(sK0) = op2(h(sK0),h(sK0)),
inference(forward_demodulation,[],[f67,f18]) ).
fof(f69,plain,
( $false
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f68,f51]) ).
fof(f70,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f69]) ).
fof(f76,plain,
( h(sK1) = op2(h(sK1),h(sK1))
| ~ spl2_1 ),
inference(resolution,[],[f29,f36]) ).
fof(f184,plain,
j(op2(op2(op2(h(sK1),h(sK1)),h(sK1)),h(sK1))) = op1(j(op2(op2(h(sK1),h(sK1)),h(sK1))),sK1),
inference(resolution,[],[f44,f60]) ).
fof(f187,plain,
( op1(j(op2(h(sK1),h(sK1))),sK1) = j(op2(op2(h(sK1),h(sK1)),h(sK1)))
| ~ spl2_1 ),
inference(forward_demodulation,[],[f184,f76]) ).
fof(f191,plain,
( j(op2(h(sK1),h(sK1))) = op1(j(h(sK1)),sK1)
| ~ spl2_1 ),
inference(forward_demodulation,[],[f187,f76]) ).
fof(f194,plain,
( op1(sK1,sK1) = j(op2(h(sK1),h(sK1)))
| ~ spl2_1 ),
inference(forward_demodulation,[],[f191,f35]) ).
fof(f197,plain,
( op1(sK1,sK1) = j(h(sK1))
| ~ spl2_1 ),
inference(forward_demodulation,[],[f194,f76]) ).
fof(f201,plain,
( sK1 = op1(sK1,sK1)
| ~ spl2_1 ),
inference(forward_demodulation,[],[f197,f35]) ).
fof(f204,plain,
( $false
| ~ spl2_1 ),
inference(forward_subsumption_resolution,[],[f201,f16]) ).
fof(f205,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f204]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f33]) ).
cnf(s2,plain,
~ spl2_2,
inference(sat_conversion,[],[f70]) ).
cnf(s5,plain,
~ spl2_1,
inference(sat_conversion,[],[f205]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s2,s5]) ).
fof(f206,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG203+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/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 19:43:43 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
% 0.09/0.27 % (1904173)Will run a generic schedule for satisfiability detection.
% 0.09/0.27 % (1904178)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=242612172_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.27 % TRYING [1]
% 0.09/0.27 % TRYING [2]
% 0.09/0.27 % TRYING [3]
% 0.09/0.27 % TRYING [4]
% 0.09/0.27 % TRYING [5]
% 0.09/0.27 % (1904179)% WARNING: option uhcvi not known.
% 0.09/0.27 % (1904181)dis+10_1_sil=32000:sp=arity:random_seed=2126054056:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.27 % (1904180)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=928052947:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.27 % (1904182)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1921161210:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.27 % (1904183)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=488255128:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.27 % (1904184)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=715028645:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.27 % (1904179)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3558716880:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.27 % TRYING [6]
% 0.09/0.27 % (1904183) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1904173-1904183"...
% 0.09/0.27 % (1904181) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1904173-1904181"...
% 0.09/0.27 % (1904183)...printing done.
% 0.09/0.27 % (1904181)...printing done.
% 0.09/0.27 % (1904183)Refutation found. Thanks to Tanya!
% 0.09/0.27 % SZS status Theorem for theBenchmark
% 0.09/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.28 % (1904183)------------------------------
% 0.09/0.28 % (1904183)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.28 % (1904183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.28 % (1904183)CaDiCaL version: 2.1.3
% 0.09/0.28 % (1904183)Termination reason: Refutation
% 0.09/0.28 % (1904183)Time elapsed: 0.006 s
% 0.09/0.28 % (1904183)Peak memory usage: 12 MB
% 0.09/0.28 % (1904183)Instructions burned: 7 (million)
% 0.09/0.28 % (1904173)Success in time 0.047 s
% 0.09/0.28 % Vampire exiting
%------------------------------------------------------------------------------