%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN056+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 01:49:09 PM UTC 2026
% Result : Theorem 3.75s 1.32s
% Output : Refutation 3.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of formulae : 38 ( 6 unt; 0 def)
% Number of atoms : 121 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 150 ( 67 ~; 57 |; 14 &)
% ( 6 <=>; 5 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 59 ( 49 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( ? [X0] : big_p(X0)
<=> ? [X1] : big_q(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel26_1) ).
fof(f2,axiom,
! [X0,X1] :
( ( big_p(X0)
& big_q(X1) )
=> ( big_r(X0)
<=> big_s(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel26_2) ).
fof(f3,conjecture,
( ! [X0] :
( big_p(X0)
=> big_r(X0) )
<=> ! [X1] :
( big_q(X1)
=> big_s(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel26) ).
fof(f4,negated_conjecture,
~ ( ! [X0] :
( big_p(X0)
=> big_r(X0) )
<=> ! [X1] :
( big_q(X1)
=> big_s(X1) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
( ! [X0] :
( big_r(X0)
| ~ big_p(X0) )
<~> ! [X1] :
( big_s(X1)
| ~ big_q(X1) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f6,plain,
! [X0,X1] :
( ( big_r(X0)
<=> big_s(X1) )
| ~ big_p(X0)
| ~ big_q(X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f7,plain,
! [X0,X1] :
( ( big_r(X0)
<=> big_s(X1) )
| ~ big_p(X0)
| ~ big_q(X1) ),
inference(flattening,[],[f6]) ).
fof(f8,plain,
( ( ? [X1] :
( ~ big_s(X1)
& big_q(X1) )
| ? [X0] :
( ~ big_r(X0)
& big_p(X0) ) )
& ( ! [X1] :
( big_s(X1)
| ~ big_q(X1) )
| ! [X0] :
( big_r(X0)
| ~ big_p(X0) ) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f9,plain,
( ( ? [X0] :
( ~ big_s(X0)
& big_q(X0) )
| ? [X1] :
( ~ big_r(X1)
& big_p(X1) ) )
& ( ! [X2] :
( big_s(X2)
| ~ big_q(X2) )
| ! [X3] :
( big_r(X3)
| ~ big_p(X3) ) ) ),
inference(rectify,[],[f8]) ).
fof(f10,plain,
( ( ( ~ big_s(sK0)
& big_q(sK0) )
| ( ~ big_r(sK1)
& big_p(sK1) ) )
& ( ! [X2] :
( big_s(X2)
| ~ big_q(X2) )
| ! [X3] :
( big_r(X3)
| ~ big_p(X3) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f9]) ).
fof(f11,plain,
( ( ? [X0] : big_p(X0)
| ! [X1] : ~ big_q(X1) )
& ( ? [X1] : big_q(X1)
| ! [X0] : ~ big_p(X0) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f12,plain,
( ( ? [X0] : big_p(X0)
| ! [X1] : ~ big_q(X1) )
& ( ? [X2] : big_q(X2)
| ! [X3] : ~ big_p(X3) ) ),
inference(rectify,[],[f11]) ).
fof(f13,plain,
( ( big_p(sK2)
| ! [X1] : ~ big_q(X1) )
& ( big_q(sK3)
| ! [X3] : ~ big_p(X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X2,sK3)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ( ( big_r(X0)
| ~ big_s(X1) )
& ( big_s(X1)
| ~ big_r(X0) ) )
| ~ big_p(X0)
| ~ big_q(X1) ),
inference(nnf_transformation,[],[f7]) ).
fof(f15,plain,
! [X2,X3] :
( big_s(X2)
| ~ big_q(X2)
| big_r(X3)
| ~ big_p(X3) ),
inference(cnf_transformation,[],[f10]) ).
fof(f16,plain,
( big_q(sK0)
| big_p(sK1) ),
inference(cnf_transformation,[],[f10]) ).
fof(f17,plain,
( big_q(sK0)
| ~ big_r(sK1) ),
inference(cnf_transformation,[],[f10]) ).
fof(f18,plain,
( big_p(sK1)
| ~ big_s(sK0) ),
inference(cnf_transformation,[],[f10]) ).
fof(f19,plain,
( ~ big_s(sK0)
| ~ big_r(sK1) ),
inference(cnf_transformation,[],[f10]) ).
fof(f20,plain,
! [X3] :
( big_q(sK3)
| ~ big_p(X3) ),
inference(cnf_transformation,[],[f13]) ).
fof(f21,plain,
! [X1] :
( big_p(sK2)
| ~ big_q(X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
! [X0,X1] :
( big_s(X1)
| ~ big_r(X0)
| ~ big_p(X0)
| ~ big_q(X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f23,plain,
! [X0,X1] :
( big_r(X0)
| ~ big_s(X1)
| ~ big_p(X0)
| ~ big_q(X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f26,plain,
! [X0,X1] :
( big_s(X1)
| ~ big_p(X0)
| ~ big_q(X1) ),
inference(forward_subsumption_resolution,[],[f22,f15]) ).
fof(f27,plain,
! [X0] :
( ~ big_p(X0)
| ~ big_q(sK0)
| ~ big_r(sK1) ),
inference(resolution,[],[f26,f19]) ).
fof(f28,plain,
! [X0] :
( ~ big_r(sK1)
| ~ big_p(X0) ),
inference(forward_subsumption_resolution,[],[f27,f17]) ).
fof(f30,plain,
! [X0,X1] :
( big_r(X0)
| ~ big_p(X0)
| ~ big_q(X1) ),
inference(forward_subsumption_resolution,[],[f23,f15]) ).
fof(f31,plain,
! [X0,X1] :
( ~ big_q(X0)
| ~ big_p(sK1)
| ~ big_p(X1) ),
inference(resolution,[],[f30,f28]) ).
fof(f34,plain,
! [X0,X1] :
( ~ big_p(sK1)
| ~ big_p(X0)
| ~ big_p(X1) ),
inference(resolution,[],[f31,f20]) ).
fof(f36,plain,
! [X0] :
( ~ big_p(sK1)
| ~ big_p(X0) ),
inference(factoring,[],[f34]) ).
fof(f39,plain,
~ big_p(sK1),
inference(factoring,[],[f36]) ).
fof(f40,plain,
~ big_s(sK0),
inference(resolution,[],[f39,f18]) ).
fof(f43,plain,
! [X0] :
( ~ big_q(sK0)
| ~ big_p(X0) ),
inference(resolution,[],[f40,f26]) ).
fof(f49,plain,
! [X0] :
( ~ big_p(X0)
| big_p(sK1) ),
inference(resolution,[],[f43,f16]) ).
fof(f50,plain,
! [X0] : ~ big_p(X0),
inference(forward_subsumption_resolution,[],[f49,f36]) ).
fof(f56,plain,
! [X0] : ~ big_q(X0),
inference(resolution,[],[f50,f21]) ).
fof(f58,plain,
big_p(sK1),
inference(resolution,[],[f56,f16]) ).
fof(f60,plain,
$false,
inference(forward_subsumption_resolution,[],[f58,f50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN056+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.19 % Computer : n017.cluster.edu
% 0.12/0.19 % Model : x86_64 x86_64
% 0.12/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.19 % Memory : 8046.5625MB
% 0.12/0.19 % OS : Linux 6.8.0-71-generic
% 0.12/0.19 % CPULimit : 300
% 0.12/0.19 % WCLimit : 300
% 0.12/0.19 % DateTime : Mon Sep 28 15:22:06 UTC 2026
% 0.12/0.20 % CPUTime :
% 0.12/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.22 Running first-order theorem proving
% 0.12/0.22 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
% 3.75/1.32 % (3630930)Detected formulas, will run a generic FOF schedule.
% 3.75/1.32 % (3631003)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=2558026718:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.75/1.32 % (3631009)dis-21_1_sil=8000:lcm=predicate:random_seed=4199707505: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)
% 3.75/1.32 % (3631006)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=345161229:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.75/1.32 % (3631004)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2862778056:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.75/1.32 % (3631002)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=4207466983:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.75/1.32 % (3631001)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=326740405:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.75/1.32 % (3631007)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1960719200:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.75/1.32 % (3631006)First to succeed.
% 3.75/1.32 % (3631009)Also succeeded, but the first one will report.
% 3.75/1.32 % (3631007)Also succeeded, but the first one will report.
% 3.75/1.32 % (3631004)Also succeeded, but the first one will report.
% 3.75/1.32 % (3631006)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3630930"
% 3.75/1.32 % (3631006)Refutation found. Thanks to Tanya!
% 3.75/1.32 % SZS status Theorem for theBenchmark
% 3.75/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.75/1.33 % (3631006)------------------------------
% 3.75/1.33 % (3631006)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.33 % (3631006)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.33 % (3631006)CaDiCaL version: 2.1.3
% 3.75/1.33 % (3631006)Termination reason: Refutation
% 3.75/1.33 % (3631006)Time elapsed: 0.002 s
% 3.75/1.33 % (3631006)Peak memory usage: 88 MB
% 3.75/1.33 % (3631006)Instructions burned: 1 (million)
% 3.75/1.33 % (3631006)------------------------------
% 3.75/1.33 % (3631006)------------------------------
% 3.75/1.33 % (3630930)Success in time 0.451 s
% 3.75/1.33 % Vampire exiting
%------------------------------------------------------------------------------