%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PUZ039-1 : TPTP v9.3.1. Bugfixed v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 12:31:20 PM UTC 2026
% Result : Unsatisfiable 0.14s 1.40s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 16 ( 10 unt; 0 def)
% Number of atoms : 22 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 7 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-12 aty)
% Number of functors : 14 ( 14 usr; 1 con; 0-2 aty)
% Number of variables : 84 ( 84 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X4,X5] :
( ~ state(X0,X1,X2,X3,X4,X5,X6,s2(X7,X8),X9,X10,e1(s(X7),X8),X11)
| state(X0,X1,X2,X3,X4,X5,X6,s2(s(X7),X8),X9,X10,e1(X7,X8),X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_down) ).
fof(f13,axiom,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X4,X5] :
( ~ state(X0,X1,X2,X3,X4,X5,X6,X7,X8,s4(X9,X10),e1(X9,s(X10)),X11)
| state(X0,X1,X2,X3,X4,X5,X6,X7,X8,s4(X9,s(X10)),e1(X9,X10),X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s4_right) ).
fof(f27,axiom,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X4,X5] :
( ~ state(X0,X1,X2,v3(X3,X4),X5,X6,X7,X8,X9,X10,e1(s(s(X3)),X4),X11)
| state(X0,X1,X2,v3(s(X3),X4),X5,X6,X7,X8,X9,X10,e1(X3,X4),X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v3_down) ).
fof(f30,axiom,
! [X2,X3,X10,X0,X1,X8,X6,X9,X7,X4,X5] :
( ~ state(X0,X1,X2,X3,v4(X4,s(X5)),X6,X7,X8,X9,X10,e1(X4,X5),e2(s(X4),X5))
| state(X0,X1,X2,X3,v4(X4,X5),X6,X7,X8,X9,X10,e1(X4,s(X5)),e2(s(X4),s(X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v4_left) ).
fof(f34,axiom,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X4,X5] :
( ~ state(X0,X1,X2,X3,X4,h(X5,s(X6)),X7,X8,X9,X10,e1(X5,X6),X11)
| state(X0,X1,X2,X3,X4,h(X5,X6),X7,X8,X9,X10,e1(X5,s(s(X6))),X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_left) ).
fof(f41,axiom,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X4,X5,X12,X13] :
( ~ state(X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,e1(X10,X11),e2(X12,X13))
| state(X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,e1(X12,X13),e2(X10,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',swap_blanks) ).
fof(f42,axiom,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_state) ).
fof(f43,negated_conjecture,
! [X2,X3,X10,X0,X1,X8,X6,X9,X7,X4,X5] : ~ state(X0,X1,X2,X3,v4(s(s(o)),s(s(o))),X4,X5,X6,X7,X8,X9,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_state) ).
fof(f44,plain,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),o),e2(s(s(s(s(o)))),s(s(s(o))))),
inference(resolution,[],[f42,f27]) ).
fof(f50,plain,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),s(s(s(o)))),e2(s(s(o)),o)),
inference(resolution,[],[f44,f41]) ).
fof(f68,plain,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(s(o)))),e1(s(s(s(s(o)))),s(s(o))),e2(s(s(o)),o)),
inference(resolution,[],[f50,f13]) ).
fof(f125,plain,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(s(o)))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(s(o)))),e1(s(s(s(o))),s(s(o))),e2(s(s(o)),o)),
inference(resolution,[],[f68,f7]) ).
fof(f252,plain,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(s(o)))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(s(o)))),e1(s(s(o)),o),e2(s(s(s(o))),s(s(o)))),
inference(resolution,[],[f125,f41]) ).
fof(f488,plain,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),o),s1(s(s(s(o))),s(o)),s2(s(s(s(s(o)))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(s(o)))),e1(s(s(o)),s(s(o))),e2(s(s(s(o))),s(s(o)))),
inference(resolution,[],[f252,f34]) ).
fof(f892,plain,
state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(o)),s(s(o))),h(s(s(o)),o),s1(s(s(s(o))),s(o)),s2(s(s(s(s(o)))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(s(o)))),e1(s(s(o)),s(s(s(o)))),e2(s(s(s(o))),s(s(s(o))))),
inference(resolution,[],[f488,f30]) ).
fof(f895,plain,
$false,
inference(forward_subsumption_resolution,[],[f892,f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ039-1 : TPTP v9.3.1. Bugfixed v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 22:35:32 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/1.40 % (236276)Input is clausal, will run a generic CNF schedule.
% 0.14/1.40 % (236285)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=861909290:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.14/1.40 % (236284)lrs+10_1_sil=8000:sp=occurrence:random_seed=2778127286:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.14/1.40 % (236283)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2184259544:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.14/1.40 % (236282)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=347206643:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.14/1.40 % (236281)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=1150475332:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.14/1.40 % (236286)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1307727678:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.14/1.40 % (236285)Instruction limit reached!
% 0.14/1.40 % (236285)------------------------------
% 0.14/1.40 % (236285)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.14/1.40 % (236285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/1.40 % (236285)CaDiCaL version: 2.1.3
% 0.14/1.40 % (236285)Termination reason: Instruction limit
% 0.14/1.40 % (236285)Termination phase: Saturation
% 0.14/1.40 % (236285)Time elapsed: 0.036 s
% 0.14/1.40 % (236285)Peak memory usage: 88 MB
% 0.14/1.40 % (236285)Instructions burned: 115 (million)
% 0.14/1.40 % (236287)dis-21_1_sil=8000:lcm=predicate:random_seed=1727524629:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 0.14/1.40 % (236286)First to succeed.
% 0.14/1.40 % (236286)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-236276"
% 0.14/1.40 % (236284)Instruction limit reached!
% 0.14/1.40 % (236284)------------------------------
% 0.14/1.40 % (236284)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.14/1.40 % (236284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/1.40 % (236284)CaDiCaL version: 2.1.3
% 0.14/1.40 % (236284)Termination reason: Instruction limit
% 0.14/1.40 % (236284)Termination phase: Saturation
% 0.14/1.40 % (236284)Time elapsed: 0.064 s
% 0.14/1.40 % (236284)Peak memory usage: 89 MB
% 0.14/1.40 % (236284)Instructions burned: 108 (million)
% 0.14/1.40 % (236287)Instruction limit reached!
% 0.14/1.40 % (236287)------------------------------
% 0.14/1.40 % (236287)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.14/1.40 % (236287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/1.40 % (236287)CaDiCaL version: 2.1.3
% 0.14/1.40 % (236287)Termination reason: Instruction limit
% 0.14/1.40 % (236287)Termination phase: Saturation
% 0.14/1.40 % (236287)Time elapsed: 0.070 s
% 0.14/1.40 % (236287)Peak memory usage: 88 MB
% 0.14/1.40 % (236287)Instructions burned: 118 (million)
% 0.14/1.40 % (236294)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=3356131087:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 0.14/1.40 % (236294)Also succeeded, but the first one will report.
% 0.14/1.40 % (236296)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2489343492:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 0.14/1.40 % (236297)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3278725213:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 0.14/1.40 % (236286)Refutation found. Thanks to Tanya!
% 0.14/1.40 % SZS status Unsatisfiable for theBenchmark
% 0.14/1.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/1.40 % (236286)------------------------------
% 0.14/1.40 % (236286)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.14/1.40 % (236286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/1.40 % (236286)CaDiCaL version: 2.1.3
% 0.14/1.40 % (236286)Termination reason: Refutation
% 0.14/1.40 % (236286)Time elapsed: 0.045 s
% 0.14/1.40 % (236286)Peak memory usage: 88 MB
% 0.14/1.40 % (236286)Instructions burned: 150 (million)
% 0.14/1.40 % (236286)------------------------------
% 0.14/1.40 % (236286)------------------------------
% 0.14/1.40 % (236276)Success in time 0.364 s
% 0.14/1.40 % Vampire exiting
%------------------------------------------------------------------------------