%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PUZ129+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 12:31:39 PM UTC 2026
% Result : Theorem 4.27s 1.50s
% Output : Refutation 5.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 1
% Syntax : Number of formulae : 39 ( 6 unt; 0 def)
% Number of atoms : 308 ( 71 equ)
% Maximal formula atoms : 36 ( 7 avg)
% Number of connectives : 428 ( 159 ~; 131 |; 116 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-1 aty)
% Number of variables : 140 ( 96 !; 44 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ! [X0] :
( ( person(X0)
& property1(X0,honest,pos)
& property1(X0,industrious,pos) )
=> ? [X1] :
( property1(X1,healthy,pos)
& X0 = X1 ) )
& ! [X2] :
( grocer(X2)
=> ~ ? [X3] :
( property1(X3,healthy,pos)
& X2 = X3 ) )
& ! [X4] :
( ( grocer(X4)
& property1(X4,industrious,pos) )
=> ? [X5] :
( property1(X5,honest,pos)
& X4 = X5 ) )
& ! [X6] :
( cyclist(X6)
=> ? [X7] :
( property1(X7,industrious,pos)
& X6 = X7 ) )
& ! [X8] :
( ( cyclist(X8)
& property1(X8,unhealthy,pos) )
=> ? [X9] :
( property1(X9,dishonest,pos)
& X8 = X9 ) )
& ! [X10] :
( ( person(X10)
& property1(X10,healthy,pos) )
=> ~ ? [X11] :
( property1(X11,unhealthy,pos)
& X10 = X11 ) )
& ! [X12] :
( ( person(X12)
& property1(X12,honest,pos) )
=> ~ ? [X13] :
( property1(X13,dishonest,pos)
& X12 = X13 ) )
& ! [X14] :
( grocer(X14)
=> ? [X15] :
( person(X15)
& X14 = X15 ) )
& ! [X16] :
( cyclist(X16)
=> ? [X17] :
( person(X17)
& X16 = X17 ) ) )
=> ! [X18] :
( grocer(X18)
=> ~ ? [X19] :
( cyclist(X19)
& X18 = X19 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
fof(f2,negated_conjecture,
~ ( ( ! [X0] :
( ( person(X0)
& property1(X0,honest,pos)
& property1(X0,industrious,pos) )
=> ? [X1] :
( property1(X1,healthy,pos)
& X0 = X1 ) )
& ! [X2] :
( grocer(X2)
=> ~ ? [X3] :
( property1(X3,healthy,pos)
& X2 = X3 ) )
& ! [X4] :
( ( grocer(X4)
& property1(X4,industrious,pos) )
=> ? [X5] :
( property1(X5,honest,pos)
& X4 = X5 ) )
& ! [X6] :
( cyclist(X6)
=> ? [X7] :
( property1(X7,industrious,pos)
& X6 = X7 ) )
& ! [X8] :
( ( cyclist(X8)
& property1(X8,unhealthy,pos) )
=> ? [X9] :
( property1(X9,dishonest,pos)
& X8 = X9 ) )
& ! [X10] :
( ( person(X10)
& property1(X10,healthy,pos) )
=> ~ ? [X11] :
( property1(X11,unhealthy,pos)
& X10 = X11 ) )
& ! [X12] :
( ( person(X12)
& property1(X12,honest,pos) )
=> ~ ? [X13] :
( property1(X13,dishonest,pos)
& X12 = X13 ) )
& ! [X14] :
( grocer(X14)
=> ? [X15] :
( person(X15)
& X14 = X15 ) )
& ! [X16] :
( cyclist(X16)
=> ? [X17] :
( person(X17)
& X16 = X17 ) ) )
=> ! [X18] :
( grocer(X18)
=> ~ ? [X19] :
( cyclist(X19)
& X18 = X19 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ? [X18] :
( ? [X19] :
( cyclist(X19)
& X18 = X19 )
& grocer(X18) )
& ! [X0] :
( ? [X1] :
( property1(X1,healthy,pos)
& X0 = X1 )
| ~ person(X0)
| ~ property1(X0,honest,pos)
| ~ property1(X0,industrious,pos) )
& ! [X2] :
( ! [X3] :
( ~ property1(X3,healthy,pos)
| X2 != X3 )
| ~ grocer(X2) )
& ! [X4] :
( ? [X5] :
( property1(X5,honest,pos)
& X4 = X5 )
| ~ grocer(X4)
| ~ property1(X4,industrious,pos) )
& ! [X6] :
( ? [X7] :
( property1(X7,industrious,pos)
& X6 = X7 )
| ~ cyclist(X6) )
& ! [X8] :
( ? [X9] :
( property1(X9,dishonest,pos)
& X8 = X9 )
| ~ cyclist(X8)
| ~ property1(X8,unhealthy,pos) )
& ! [X10] :
( ! [X11] :
( ~ property1(X11,unhealthy,pos)
| X10 != X11 )
| ~ person(X10)
| ~ property1(X10,healthy,pos) )
& ! [X12] :
( ! [X13] :
( ~ property1(X13,dishonest,pos)
| X12 != X13 )
| ~ person(X12)
| ~ property1(X12,honest,pos) )
& ! [X14] :
( ? [X15] :
( person(X15)
& X14 = X15 )
| ~ grocer(X14) )
& ! [X16] :
( ? [X17] :
( person(X17)
& X16 = X17 )
| ~ cyclist(X16) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
( ? [X18] :
( ? [X19] :
( cyclist(X19)
& X18 = X19 )
& grocer(X18) )
& ! [X0] :
( ? [X1] :
( property1(X1,healthy,pos)
& X0 = X1 )
| ~ person(X0)
| ~ property1(X0,honest,pos)
| ~ property1(X0,industrious,pos) )
& ! [X2] :
( ! [X3] :
( ~ property1(X3,healthy,pos)
| X2 != X3 )
| ~ grocer(X2) )
& ! [X4] :
( ? [X5] :
( property1(X5,honest,pos)
& X4 = X5 )
| ~ grocer(X4)
| ~ property1(X4,industrious,pos) )
& ! [X6] :
( ? [X7] :
( property1(X7,industrious,pos)
& X6 = X7 )
| ~ cyclist(X6) )
& ! [X8] :
( ? [X9] :
( property1(X9,dishonest,pos)
& X8 = X9 )
| ~ cyclist(X8)
| ~ property1(X8,unhealthy,pos) )
& ! [X10] :
( ! [X11] :
( ~ property1(X11,unhealthy,pos)
| X10 != X11 )
| ~ person(X10)
| ~ property1(X10,healthy,pos) )
& ! [X12] :
( ! [X13] :
( ~ property1(X13,dishonest,pos)
| X12 != X13 )
| ~ person(X12)
| ~ property1(X12,honest,pos) )
& ! [X14] :
( ? [X15] :
( person(X15)
& X14 = X15 )
| ~ grocer(X14) )
& ! [X16] :
( ? [X17] :
( person(X17)
& X16 = X17 )
| ~ cyclist(X16) ) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
( ? [X0] :
( ? [X1] :
( cyclist(X1)
& X0 = X1 )
& grocer(X0) )
& ! [X2] :
( ? [X3] :
( property1(X3,healthy,pos)
& X2 = X3 )
| ~ person(X2)
| ~ property1(X2,honest,pos)
| ~ property1(X2,industrious,pos) )
& ! [X4] :
( ! [X5] :
( ~ property1(X5,healthy,pos)
| X4 != X5 )
| ~ grocer(X4) )
& ! [X6] :
( ? [X7] :
( property1(X7,honest,pos)
& X6 = X7 )
| ~ grocer(X6)
| ~ property1(X6,industrious,pos) )
& ! [X8] :
( ? [X9] :
( property1(X9,industrious,pos)
& X8 = X9 )
| ~ cyclist(X8) )
& ! [X10] :
( ? [X11] :
( property1(X11,dishonest,pos)
& X10 = X11 )
| ~ cyclist(X10)
| ~ property1(X10,unhealthy,pos) )
& ! [X12] :
( ! [X13] :
( ~ property1(X13,unhealthy,pos)
| X12 != X13 )
| ~ person(X12)
| ~ property1(X12,healthy,pos) )
& ! [X14] :
( ! [X15] :
( ~ property1(X15,dishonest,pos)
| X14 != X15 )
| ~ person(X14)
| ~ property1(X14,honest,pos) )
& ! [X16] :
( ? [X17] :
( person(X17)
& X16 = X17 )
| ~ grocer(X16) )
& ! [X18] :
( ? [X19] :
( person(X19)
& X18 = X19 )
| ~ cyclist(X18) ) ),
inference(rectify,[],[f4]) ).
fof(f6,plain,
( cyclist(sK1)
& sK0 = sK1
& grocer(sK0)
& ! [X2] :
( ( property1(sK2(X2),healthy,pos)
& sK2(X2) = X2 )
| ~ person(X2)
| ~ property1(X2,honest,pos)
| ~ property1(X2,industrious,pos) )
& ! [X4] :
( ! [X5] :
( ~ property1(X5,healthy,pos)
| X4 != X5 )
| ~ grocer(X4) )
& ! [X6] :
( ( property1(sK3(X6),honest,pos)
& sK3(X6) = X6 )
| ~ grocer(X6)
| ~ property1(X6,industrious,pos) )
& ! [X8] :
( ( property1(sK4(X8),industrious,pos)
& sK4(X8) = X8 )
| ~ cyclist(X8) )
& ! [X10] :
( ( property1(sK5(X10),dishonest,pos)
& sK5(X10) = X10 )
| ~ cyclist(X10)
| ~ property1(X10,unhealthy,pos) )
& ! [X12] :
( ! [X13] :
( ~ property1(X13,unhealthy,pos)
| X12 != X13 )
| ~ person(X12)
| ~ property1(X12,healthy,pos) )
& ! [X14] :
( ! [X15] :
( ~ property1(X15,dishonest,pos)
| X14 != X15 )
| ~ person(X14)
| ~ property1(X14,honest,pos) )
& ! [X16] :
( ( person(sK6(X16))
& sK6(X16) = X16 )
| ~ grocer(X16) )
& ! [X18] :
( ( person(sK7(X18))
& sK7(X18) = X18 )
| ~ cyclist(X18) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X3,sK2(X2)),skolemize(X7,sK3(X6)),skolemize(X9,sK4(X8)),skolemize(X11,sK5(X10)),skolemize(X17,sK6(X16)),skolemize(X19,sK7(X18))],[f5]) ).
fof(f7,plain,
! [X18] :
( sK7(X18) = X18
| ~ cyclist(X18) ),
inference(cnf_transformation,[],[f6]) ).
fof(f8,plain,
! [X18] :
( person(sK7(X18))
| ~ cyclist(X18) ),
inference(cnf_transformation,[],[f6]) ).
fof(f15,plain,
! [X8] :
( sK4(X8) = X8
| ~ cyclist(X8) ),
inference(cnf_transformation,[],[f6]) ).
fof(f16,plain,
! [X8] :
( property1(sK4(X8),industrious,pos)
| ~ cyclist(X8) ),
inference(cnf_transformation,[],[f6]) ).
fof(f17,plain,
! [X6] :
( ~ property1(X6,industrious,pos)
| ~ grocer(X6)
| sK3(X6) = X6 ),
inference(cnf_transformation,[],[f6]) ).
fof(f18,plain,
! [X6] :
( property1(sK3(X6),honest,pos)
| ~ grocer(X6)
| ~ property1(X6,industrious,pos) ),
inference(cnf_transformation,[],[f6]) ).
fof(f19,plain,
! [X4,X5] :
( ~ property1(X5,healthy,pos)
| X4 != X5
| ~ grocer(X4) ),
inference(cnf_transformation,[],[f6]) ).
fof(f20,plain,
! [X2] :
( ~ property1(X2,industrious,pos)
| ~ person(X2)
| ~ property1(X2,honest,pos)
| sK2(X2) = X2 ),
inference(cnf_transformation,[],[f6]) ).
fof(f21,plain,
! [X2] :
( property1(sK2(X2),healthy,pos)
| ~ person(X2)
| ~ property1(X2,honest,pos)
| ~ property1(X2,industrious,pos) ),
inference(cnf_transformation,[],[f6]) ).
fof(f22,plain,
grocer(sK0),
inference(cnf_transformation,[],[f6]) ).
fof(f23,plain,
sK0 = sK1,
inference(cnf_transformation,[],[f6]) ).
fof(f24,plain,
cyclist(sK1),
inference(cnf_transformation,[],[f6]) ).
fof(f25,plain,
grocer(sK1),
inference(definition_unfolding,[],[f22,f23]) ).
fof(f26,plain,
! [X5] :
( ~ property1(X5,healthy,pos)
| ~ grocer(X5) ),
inference(equality_resolution,[],[f19]) ).
fof(f29,plain,
! [X0] :
( person(X0)
| ~ cyclist(X0)
| ~ cyclist(X0) ),
inference(superposition,[],[f8,f7]) ).
fof(f30,plain,
! [X0] :
( person(X0)
| ~ cyclist(X0) ),
inference(duplicate_literal_removal,[],[f29]) ).
fof(f33,plain,
! [X0] :
( property1(X0,industrious,pos)
| ~ cyclist(X0)
| ~ cyclist(X0) ),
inference(superposition,[],[f16,f15]) ).
fof(f34,plain,
! [X0] :
( property1(X0,industrious,pos)
| ~ cyclist(X0) ),
inference(duplicate_literal_removal,[],[f33]) ).
fof(f36,plain,
! [X0] :
( sK3(X0) = X0
| ~ grocer(X0)
| ~ cyclist(X0) ),
inference(resolution,[],[f17,f34]) ).
fof(f38,plain,
! [X0] :
( property1(X0,honest,pos)
| ~ grocer(X0)
| ~ property1(X0,industrious,pos)
| ~ grocer(X0)
| ~ cyclist(X0) ),
inference(superposition,[],[f18,f36]) ).
fof(f39,plain,
! [X0] :
( property1(X0,honest,pos)
| ~ grocer(X0)
| ~ property1(X0,industrious,pos)
| ~ cyclist(X0) ),
inference(duplicate_literal_removal,[],[f38]) ).
fof(f40,plain,
! [X0] :
( property1(X0,honest,pos)
| ~ grocer(X0)
| ~ cyclist(X0) ),
inference(forward_subsumption_resolution,[],[f39,f34]) ).
fof(f47,plain,
! [X0] :
( ~ person(X0)
| ~ property1(X0,honest,pos)
| sK2(X0) = X0
| ~ cyclist(X0) ),
inference(resolution,[],[f20,f34]) ).
fof(f48,plain,
! [X0] :
( ~ property1(X0,honest,pos)
| sK2(X0) = X0
| ~ cyclist(X0) ),
inference(forward_subsumption_resolution,[],[f47,f30]) ).
fof(f53,plain,
! [X0] :
( sK2(X0) = X0
| ~ cyclist(X0)
| ~ grocer(X0)
| ~ cyclist(X0) ),
inference(resolution,[],[f48,f40]) ).
fof(f55,plain,
! [X0] :
( sK2(X0) = X0
| ~ cyclist(X0)
| ~ grocer(X0) ),
inference(duplicate_literal_removal,[],[f53]) ).
fof(f56,plain,
! [X0] :
( property1(X0,healthy,pos)
| ~ person(X0)
| ~ property1(X0,honest,pos)
| ~ property1(X0,industrious,pos)
| ~ cyclist(X0)
| ~ grocer(X0) ),
inference(superposition,[],[f21,f55]) ).
fof(f57,plain,
! [X0] :
( ~ person(X0)
| ~ property1(X0,honest,pos)
| ~ property1(X0,industrious,pos)
| ~ cyclist(X0)
| ~ grocer(X0) ),
inference(forward_subsumption_resolution,[],[f56,f26]) ).
fof(f58,plain,
! [X0] :
( ~ property1(X0,honest,pos)
| ~ property1(X0,industrious,pos)
| ~ cyclist(X0)
| ~ grocer(X0) ),
inference(forward_subsumption_resolution,[],[f57,f30]) ).
fof(f59,plain,
! [X0] :
( ~ property1(X0,industrious,pos)
| ~ cyclist(X0)
| ~ grocer(X0) ),
inference(forward_subsumption_resolution,[],[f58,f40]) ).
fof(f60,plain,
! [X0] :
( ~ cyclist(X0)
| ~ grocer(X0) ),
inference(forward_subsumption_resolution,[],[f59,f34]) ).
fof(f64,plain,
~ grocer(sK1),
inference(resolution,[],[f60,f24]) ).
fof(f65,plain,
$false,
inference(forward_subsumption_resolution,[],[f64,f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : PUZ129+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.42 % Computer : n006.cluster.edu
% 0.18/0.42 % Model : x86_64 x86_64
% 0.18/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.42 % Memory : 8046.5625MB
% 0.18/0.42 % OS : Linux 6.8.0-71-generic
% 0.18/0.42 % CPULimit : 300
% 0.18/0.42 % WCLimit : 300
% 0.18/0.42 % DateTime : Sun Sep 27 22:44:10 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.48 Running first-order theorem proving
% 0.24/0.48 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.27/1.50 % (3400335)Detected formulas, will run a generic FOF schedule.
% 4.27/1.50 % (3400340)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1103768962:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.27/1.50 % (3400341)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=496532708:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.27/1.50 % (3400342)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=777426044:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.27/1.50 % (3400344)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=346270765:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.27/1.50 % (3400343)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3091455811:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.27/1.50 % (3400345)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1413519849:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.27/1.50 % (3400346)dis-21_1_sil=8000:lcm=predicate:random_seed=2157378413:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 4.27/1.50 % (3400346)Refutation not found, incomplete strategy
% 4.27/1.50 % (3400346)------------------------------
% 4.27/1.50 % (3400346)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.27/1.50 % (3400346)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.27/1.50 % (3400346)CaDiCaL version: 2.1.3
% 4.27/1.50 % (3400346)Termination reason: Refutation not found, incomplete strategy
% 4.27/1.50 % (3400346)Time elapsed: 0.003 s
% 4.27/1.50 % (3400346)Peak memory usage: 88 MB
% 4.27/1.50 % (3400346)Instructions burned: 1 (million)
% 4.27/1.50 % (3400343)Also succeeded, but the first one will report.
% 4.27/1.50 % (3400344)First to succeed.
% 4.27/1.50 % (3400345)Also succeeded, but the first one will report.
% 4.27/1.50 % (3400344)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3400335"
% 4.27/1.50 % (3400346)------------------------------
% 4.27/1.50 % (3400346)------------------------------
% 4.27/1.50 % (3400344)Refutation found. Thanks to Tanya!
% 4.27/1.50 % SZS status Theorem for theBenchmark
% 4.27/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 5.10/1.64 % (3400344)------------------------------
% 5.10/1.64 % (3400344)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.10/1.64 % (3400344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.10/1.64 % (3400344)CaDiCaL version: 2.1.3
% 5.10/1.64 % (3400344)Termination reason: Refutation
% 5.10/1.64 % (3400344)Time elapsed: 0.006 s
% 5.10/1.64 % (3400344)Peak memory usage: 88 MB
% 5.10/1.64 % (3400344)Instructions burned: 4 (million)
% 5.10/1.64 % (3400344)------------------------------
% 5.10/1.64 % (3400344)------------------------------
% 5.10/1.64 % (3400335)Success in time 0.633 s
% 5.10/1.64 % Vampire exiting
%------------------------------------------------------------------------------