%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW196+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 01:29:49 PM UTC 2026
% Result : Theorem 3.97s 1.35s
% Output : Refutation 3.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 13 unt; 2 def)
% Number of atoms : 31 ( 8 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 22 ( 13 ~; 6 |; 0 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 6 ( 0 sgn 4 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0] : v_na____ = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096EX_Am_O_An_A_061_A2_A_K_Am_096) ).
fof(f1171,axiom,
( ? [X0] : v_na____ = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0)
=> v_thesis____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f1172,conjecture,
v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(f1173,negated_conjecture,
~ v_thesis____,
inference(negated_conjecture,[status(cth)],[f1172]) ).
fof(f1176,plain,
~ v_thesis____,
inference(flattening,[],[f1173]) ).
fof(f2114,plain,
( v_thesis____
| ! [X0] : v_na____ != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0) ),
inference(ennf_transformation,[],[f1171]) ).
fof(f2118,plain,
v_na____ = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f1]) ).
fof(f2513,plain,
v_na____ = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),sK2),
inference(cnf_transformation,[],[f2118]) ).
fof(f4165,plain,
! [X0] :
( v_thesis____
| v_na____ != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0) ),
inference(cnf_transformation,[],[f2114]) ).
fof(f4166,plain,
~ v_thesis____,
inference(cnf_transformation,[],[f1176]) ).
fof(f4358,definition,
( spl23_1
<=> ! [X0] : v_na____ != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0) ),
introduced(definition,[new_symbols(definition,[spl23_1])],[avatar_definition]) ).
fof(f4359,plain,
( ! [X0] : v_na____ != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0)
| ~ spl23_1 ),
inference(avatar_component_clause,[],[f4358]) ).
fof(f4361,definition,
( spl23_2
<=> v_thesis____ ),
introduced(definition,[new_symbols(definition,[spl23_2])],[avatar_definition]) ).
fof(f4364,plain,
( spl23_1
| spl23_2 ),
inference(avatar_split_clause,[],[f4165,f4361,f4358]) ).
fof(f4376,plain,
~ spl23_2,
inference(avatar_split_clause,[],[f4166,f4361]) ).
fof(f4418,plain,
( $false
| ~ spl23_1 ),
inference(forward_subsumption_resolution,[],[f2513,f4359]) ).
fof(f4419,plain,
~ spl23_1,
inference(avatar_contradiction_clause,[],[f4418]) ).
cnf(s1,plain,
( spl23_1
| spl23_2 ),
inference(sat_conversion,[],[f4364]) ).
cnf(s5,plain,
~ spl23_2,
inference(sat_conversion,[],[f4376]) ).
cnf(s6,plain,
~ spl23_1,
inference(sat_conversion,[],[f4419]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s5,s6]) ).
fof(f4420,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW196+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.16 % Computer : n013.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Mon Sep 28 13:16:37 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running first-order theorem proving
% 0.08/0.20 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
% 3.97/1.35 % (1169918)Detected formulas, will run a generic FOF schedule.
% 3.97/1.35 % (1169923)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=1293309341:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.97/1.35 % (1169928)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3136449774:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.97/1.35 % (1169925)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=2884385211:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.97/1.35 % (1169924)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=381125763:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.97/1.35 % (1169926)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4276201483:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.97/1.35 % (1169927)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1351119871:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.97/1.35 % (1169929)dis-21_1_sil=8000:lcm=predicate:random_seed=3390133110: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)
% 3.97/1.35 % (1169928)First to succeed.
% 3.97/1.35 % (1169928)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1169918"
% 3.97/1.35 % (1169926)Instruction limit reached!
% 3.97/1.35 % (1169926)------------------------------
% 3.97/1.35 % (1169926)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.97/1.35 % (1169926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.97/1.35 % (1169926)CaDiCaL version: 2.1.3
% 3.97/1.35 % (1169926)Termination reason: Instruction limit
% 3.97/1.35 % (1169926)Termination phase: Saturation
% 3.97/1.35 % (1169926)Time elapsed: 0.065 s
% 3.97/1.35 % (1169926)Peak memory usage: 90 MB
% 3.97/1.35 % (1169926)Instructions burned: 109 (million)
% 3.97/1.35 % (1169927)Instruction limit reached!
% 3.97/1.35 % (1169927)------------------------------
% 3.97/1.35 % (1169927)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.97/1.35 % (1169927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.97/1.35 % (1169927)CaDiCaL version: 2.1.3
% 3.97/1.35 % (1169927)Termination reason: Instruction limit
% 3.97/1.35 % (1169927)Termination phase: Saturation
% 3.97/1.35 % (1169927)Time elapsed: 0.071 s
% 3.97/1.35 % (1169927)Peak memory usage: 89 MB
% 3.97/1.35 % (1169927)Instructions burned: 119 (million)
% 3.97/1.35 % (1169929)Instruction limit reached!
% 3.97/1.35 % (1169929)------------------------------
% 3.97/1.35 % (1169929)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.97/1.35 % (1169929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.97/1.35 % (1169929)CaDiCaL version: 2.1.3
% 3.97/1.35 % (1169929)Termination reason: Instruction limit
% 3.97/1.35 % (1169929)Termination phase: Saturation
% 3.97/1.35 % (1169929)Time elapsed: 0.065 s
% 3.97/1.35 % (1169929)Peak memory usage: 91 MB
% 3.97/1.35 % (1169929)Instructions burned: 130 (million)
% 3.97/1.35 % (1169937)lrs+10_1_sil=8000:sp=occurrence:random_seed=1521411282:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.97/1.35 % (1169939)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3125897382:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.97/1.35 % (1169938)lrs+10_1_sil=32000:urr=on:br=off:random_seed=812117813:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.97/1.35 % (1169938)Refutation not found, incomplete strategy
% 3.97/1.35 % (1169938)------------------------------
% 3.97/1.35 % (1169938)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.97/1.35 % (1169938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.97/1.35 % (1169938)CaDiCaL version: 2.1.3
% 3.97/1.35 % (1169938)Termination reason: Refutation not found, incomplete strategy
% 3.97/1.35 % (1169938)Time elapsed: 0.008 s
% 3.97/1.35 % (1169938)Peak memory usage: 89 MB
% 3.97/1.35 % (1169938)Instructions burned: 15 (million)
% 3.97/1.35 % (1169928)Refutation found. Thanks to Tanya!
% 3.97/1.35 % SZS status Theorem for theBenchmark
% 3.97/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 3.97/1.35 % (1169928)------------------------------
% 3.97/1.35 % (1169928)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.97/1.35 % (1169928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.97/1.35 % (1169928)CaDiCaL version: 2.1.3
% 3.97/1.35 % (1169928)Termination reason: Refutation
% 3.97/1.35 % (1169928)Time elapsed: 0.046 s
% 3.97/1.35 % (1169928)Peak memory usage: 91 MB
% 3.97/1.35 % (1169928)Instructions burned: 92 (million)
% 3.97/1.35 % (1169928)------------------------------
% 3.97/1.35 % (1169928)------------------------------
% 3.97/1.35 % (1169918)Success in time 0.514 s
% 3.97/1.35 % Vampire exiting
%------------------------------------------------------------------------------