%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN040+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 : n009.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 01:49:03 PM UTC 2026
% Result : Theorem 0.19s 1.20s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 13 ( 4 unt; 0 def)
% Number of atoms : 42 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 50 ( 21 ~; 16 |; 6 &)
% ( 2 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 0 ( 0 avg)
% Number of predicates : 3 ( 2 usr; 3 prp; 0-0 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 0 ( 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( p
=> q )
<=> ( ~ q
=> ~ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel1) ).
fof(f2,negated_conjecture,
~ ( ( p
=> q )
<=> ( ~ q
=> ~ p ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ( q
| ~ p )
<~> ( ~ p
| q ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
( ( ( p
& ~ q )
| ( ~ q
& p ) )
& ( ~ p
| q
| q
| ~ p ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f5,plain,
( ( ( p
& ~ q )
| ( ~ q
& p ) )
& ( ~ p
| q
| q
| ~ p ) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
( ~ p
| q
| q
| ~ p ),
inference(cnf_transformation,[],[f5]) ).
fof(f8,plain,
( ~ q
| ~ q ),
inference(cnf_transformation,[],[f5]) ).
fof(f9,plain,
( p
| p ),
inference(cnf_transformation,[],[f5]) ).
fof(f11,plain,
( ~ p
| q ),
inference(duplicate_literal_removal,[],[f6]) ).
fof(f12,plain,
~ q,
inference(duplicate_literal_removal,[],[f8]) ).
fof(f13,plain,
p,
inference(duplicate_literal_removal,[],[f9]) ).
fof(f14,plain,
q,
inference(forward_subsumption_resolution,[],[f11,f13]) ).
fof(f15,plain,
$false,
inference(forward_subsumption_resolution,[],[f14,f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN040+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n009.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 15:24:45 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 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
% 0.19/1.20 % (3145641)Detected formulas, will run a generic FOF schedule.
% 0.19/1.20 % (3145648)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=512634367:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.19/1.20 % (3145652)dis-21_1_sil=8000:lcm=predicate:random_seed=1787041361: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)
% 0.19/1.20 % (3145647)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=829803407:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.19/1.20 % (3145649)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1267401602:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.19/1.20 % (3145650)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3706886315:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.19/1.20 % (3145651)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=577949931:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.19/1.20 % (3145646)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=3730939416:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.19/1.20 % (3145650)First to succeed.
% 0.19/1.20 % (3145649)Also succeeded, but the first one will report.
% 0.19/1.20 % (3145651)Also succeeded, but the first one will report.
% 0.19/1.20 % (3145652)Also succeeded, but the first one will report.
% 0.19/1.20 % (3145650)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3145641"
% 0.19/1.20 [W928 15:24:45.635998763 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 0.19/1.20 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.19/1.20 [W928 15:24:45.636034545 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 0.19/1.20 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.19/1.20 [W928 15:24:45.636055919 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 0.19/1.20 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.19/1.20 [W928 15:24:45.636061721 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 0.19/1.20 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.19/1.20 [W928 15:24:45.636080837 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 0.19/1.20 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.19/1.20 [W928 15:24:45.636086211 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 0.19/1.20 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.19/1.20 [W928 15:24:45.636098932 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 0.19/1.20 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.19/1.20 [W928 15:24:45.636104422 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 0.19/1.20 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.19/1.20 % (3145650)Refutation found. Thanks to Tanya!
% 0.19/1.20 % SZS status Theorem for theBenchmark
% 0.19/1.20 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.20 % (3145650)------------------------------
% 0.19/1.20 % (3145650)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.20 % (3145650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.20 % (3145650)CaDiCaL version: 2.1.3
% 0.19/1.20 % (3145650)Termination reason: Refutation
% 0.19/1.20 % (3145650)Time elapsed: 0.001 s
% 0.19/1.20 % (3145650)Peak memory usage: 87 MB
% 0.19/1.20 % (3145650)------------------------------
% 0.19/1.20 % (3145650)------------------------------
% 0.19/1.20 % (3145641)Success in time 0.437 s
% 0.19/1.20 % Vampire exiting
%------------------------------------------------------------------------------