%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN327+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 01:50:13 PM UTC 2026
% Result : Theorem 2.53s 1.04s
% Output : Refutation 2.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 10 ( 3 unt; 0 def)
% Number of atoms : 43 ( 0 equ)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 54 ( 21 ~; 9 |; 16 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 16 ( 10 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
? [X1] :
! [X2] :
( big_f(X1,X0)
=> ( ( big_f(X0,X2)
=> big_f(X0,X1) )
& ( big_f(X0,X1)
=> ( ~ big_f(X0,X2)
=> ( big_f(X1,X0)
& big_f(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_12_2) ).
fof(f2,negated_conjecture,
~ ! [X0] :
? [X1] :
! [X2] :
( big_f(X1,X0)
=> ( ( big_f(X0,X2)
=> big_f(X0,X1) )
& ( big_f(X0,X1)
=> ( ~ big_f(X0,X2)
=> ( big_f(X1,X0)
& big_f(X2,X1) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [X0] :
! [X1] :
? [X2] :
( ( ( ~ big_f(X0,X1)
& big_f(X0,X2) )
| ( ( ~ big_f(X1,X0)
| ~ big_f(X2,X1) )
& ~ big_f(X0,X2)
& big_f(X0,X1) ) )
& big_f(X1,X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
? [X0] :
! [X1] :
? [X2] :
( ( ( ~ big_f(X0,X1)
& big_f(X0,X2) )
| ( ( ~ big_f(X1,X0)
| ~ big_f(X2,X1) )
& ~ big_f(X0,X2)
& big_f(X0,X1) ) )
& big_f(X1,X0) ),
inference(flattening,[],[f3]) ).
fof(f5,plain,
! [X1] :
( ( ( ~ big_f(sK0,X1)
& big_f(sK0,sK1(X1)) )
| ( ( ~ big_f(X1,sK0)
| ~ big_f(sK1(X1),X1) )
& ~ big_f(sK0,sK1(X1))
& big_f(sK0,X1) ) )
& big_f(X1,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X2,sK1(X1))],[f4]) ).
fof(f6,plain,
! [X1] : big_f(X1,sK0),
inference(cnf_transformation,[],[f5]) ).
fof(f12,plain,
! [X1] :
( ~ big_f(sK0,X1)
| ~ big_f(X1,sK0)
| ~ big_f(sK1(X1),X1) ),
inference(cnf_transformation,[],[f5]) ).
fof(f14,plain,
! [X1] :
( ~ big_f(sK1(X1),X1)
| ~ big_f(sK0,X1) ),
inference(forward_subsumption_resolution,[],[f12,f6]) ).
fof(f16,plain,
~ big_f(sK0,sK0),
inference(resolution,[],[f14,f6]) ).
fof(f17,plain,
$false,
inference(forward_subsumption_resolution,[],[f16,f6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN327+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 % Computer : n015.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Mon Sep 28 15:45:32 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running first-order theorem proving
% 0.07/0.23 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
% 2.53/1.04 % (2736101)Detected formulas, will run a generic FOF schedule.
% 2.53/1.04 % (2736182)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1438225930:i=109:sd=1:ins=1:gsp=on:ss=axioms_3000 on theBenchmark for (3000ds/109Mi)
% 2.53/1.04 % (2736182)First to succeed.
% 2.53/1.04 % (2736182)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2736101"
% 2.53/1.04 % (2736179)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=3882969665:i=141193_3000 on theBenchmark for (3000ds/141193Mi)
% 2.53/1.04 % (2736181)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=1220928745:i=141695:sd=1:nm=32:gsp=on:ss=included_3000 on theBenchmark for (3000ds/141695Mi)
% 2.53/1.04 % (2736180)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=1383669633:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/134677Mi)
% 2.53/1.04 % (2736185)dis-21_1_sil=8000:lcm=predicate:random_seed=482445848:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_3000 on theBenchmark for (3000ds/129Mi)
% 2.53/1.04 % (2736184)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3043048228:s2a=on:i=139:gtg=position_3000 on theBenchmark for (3000ds/139Mi)
% 2.53/1.04 % (2736183)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1026416185:i=119:av=off:ss=axioms_3000 on theBenchmark for (3000ds/119Mi)
% 2.53/1.04 % (2736183)Also succeeded, but the first one will report.
% 2.53/1.04 % (2736185)Also succeeded, but the first one will report.
% 2.53/1.04 % (2736184)Also succeeded, but the first one will report.
% 2.53/1.04 % (2736182)Refutation found. Thanks to Tanya!
% 2.53/1.04 % SZS status Theorem for theBenchmark
% 2.53/1.04 % SZS output start Proof for theBenchmark
% See solution above
% 2.53/1.04 % (2736182)------------------------------
% 2.53/1.04 % (2736182)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.04 % (2736182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.04 % (2736182)CaDiCaL version: 2.1.3
% 2.53/1.04 % (2736182)Termination reason: Refutation
% 2.53/1.04 % (2736182)Time elapsed: 0.001 s
% 2.53/1.04 % (2736182)Peak memory usage: 88 MB
% 2.53/1.04 % (2736182)------------------------------
% 2.53/1.04 % (2736182)------------------------------
% 2.53/1.04 % (2736101)Success in time 0.268 s
% 2.53/1.04 % Vampire exiting
%------------------------------------------------------------------------------