%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG001-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 12:35:03 PM UTC 2026
% Result : Unsatisfiable 5.74s 1.77s
% Output : Refutation 5.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of formulae : 14 ( 11 unt; 0 def)
% Number of atoms : 25 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 27 ( 16 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 29 ( 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] : sum(additive_identity,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).
fof(f3,axiom,
! [X0] : sum(X0,additive_identity,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
fof(f4,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
fof(f5,axiom,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_addition) ).
fof(f7,axiom,
! [X0] : sum(X0,additive_inverse(X0),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse2) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4,X5] :
( sum(X0,X4,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X2,X3,X5)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition1) ).
fof(f13,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( sum(X2,X4,X6)
| ~ product(X0,X3,X4)
| ~ sum(X1,X3,X5)
| ~ product(X0,X5,X6)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
fof(f14,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( product(X0,X5,X6)
| ~ product(X0,X3,X4)
| ~ sum(X1,X3,X5)
| ~ sum(X2,X4,X6)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
fof(f18,negated_conjecture,
~ product(a,additive_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem) ).
fof(f25,plain,
~ sum(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity),
inference(unit_resulting_resolution,[],[f14,f4,f3,f4,f18]) ).
fof(f78,plain,
~ sum(add(multiply(a,additive_identity),multiply(a,additive_identity)),additive_identity,additive_identity),
inference(unit_resulting_resolution,[],[f8,f5,f3,f25]) ).
fof(f818,plain,
! [X0] : ~ sum(add(multiply(a,additive_identity),multiply(a,additive_identity)),X0,X0),
inference(unit_resulting_resolution,[],[f8,f7,f7,f78]) ).
fof(f4213,plain,
! [X0] : ~ product(X0,additive_identity,add(multiply(a,additive_identity),multiply(a,additive_identity))),
inference(unit_resulting_resolution,[],[f13,f4,f4,f3,f818]) ).
fof(f5250,plain,
$false,
inference(unit_resulting_resolution,[],[f14,f2,f4,f4,f5,f4213]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG001-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n019.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 22:57:48 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 5.74/1.77 % (3502990)Input is clausal, will run a generic CNF schedule.
% 5.74/1.77 % (3502999)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3115673855:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.74/1.77 % (3502996)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=949808644:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.74/1.77 % (3503000)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=108071779:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.74/1.77 % (3502998)lrs+10_1_sil=8000:sp=occurrence:random_seed=1019180379:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.74/1.77 % (3503001)dis-21_1_sil=8000:lcm=predicate:random_seed=511222919: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)
% 5.74/1.77 % (3502997)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=556653260:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.74/1.77 % (3502995)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=3532775282:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.74/1.77 % (3502999)Instruction limit reached!
% 5.74/1.77 % (3502999)------------------------------
% 5.74/1.77 % (3502999)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.74/1.77 % (3502999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/1.77 % (3502999)CaDiCaL version: 2.1.3
% 5.74/1.77 % (3502999)Termination reason: Instruction limit
% 5.74/1.77 % (3502999)Termination phase: Saturation
% 5.74/1.77 % (3502999)Time elapsed: 0.034 s
% 5.74/1.77 % (3502999)Peak memory usage: 88 MB
% 5.74/1.77 % (3502999)Instructions burned: 118 (million)
% 5.74/1.77 % (3503001)Instruction limit reached!
% 5.74/1.77 % (3503001)------------------------------
% 5.74/1.77 % (3503001)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.74/1.77 % (3503001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/1.77 % (3503001)CaDiCaL version: 2.1.3
% 5.74/1.77 % (3503001)Termination reason: Instruction limit
% 5.74/1.77 % (3503001)Termination phase: Saturation
% 5.74/1.77 % (3503001)Time elapsed: 0.060 s
% 5.74/1.77 % (3503001)Peak memory usage: 88 MB
% 5.74/1.77 % (3503001)Instructions burned: 119 (million)
% 5.74/1.77 % (3502998)Instruction limit reached!
% 5.74/1.77 % (3502998)------------------------------
% 5.74/1.77 % (3502998)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.74/1.77 % (3502998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/1.77 % (3502998)CaDiCaL version: 2.1.3
% 5.74/1.77 % (3502998)Termination reason: Instruction limit
% 5.74/1.77 % (3502998)Termination phase: Saturation
% 5.74/1.77 % (3502998)Time elapsed: 0.066 s
% 5.74/1.77 % (3502998)Peak memory usage: 87 MB
% 5.74/1.77 % (3502998)Instructions burned: 107 (million)
% 5.74/1.77 % (3503000)Instruction limit reached!
% 5.74/1.77 % (3503000)------------------------------
% 5.74/1.77 % (3503000)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.74/1.77 % (3503000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/1.77 % (3503000)CaDiCaL version: 2.1.3
% 5.74/1.77 % (3503000)Termination reason: Instruction limit
% 5.74/1.77 % (3503000)Termination phase: Saturation
% 5.74/1.77 % (3503000)Time elapsed: 0.099 s
% 5.74/1.77 % (3503000)Peak memory usage: 88 MB
% 5.74/1.77 % (3503000)Instructions burned: 180 (million)
% 5.74/1.77 % (3503009)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=2705939008:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 5.74/1.77 % (3503009)Refutation not found, incomplete strategy
% 5.74/1.77 % (3503009)------------------------------
% 5.74/1.77 % (3503009)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.74/1.77 % (3503009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/1.77 % (3503009)CaDiCaL version: 2.1.3
% 5.74/1.77 % (3503009)Termination reason: Refutation not found, incomplete strategy
% 5.74/1.77 % (3503009)Time elapsed: 0.001 s
% 5.74/1.77 % (3503009)Peak memory usage: 87 MB
% 5.74/1.77 % (3503010)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=4124161182: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)
% 5.74/1.77 % (3503011)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2656525104:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.74/1.77 % (3503009)------------------------------
% 5.74/1.77 % (3503009)------------------------------
% 5.74/1.77 % (3503012)lrs+10_64_to=lpo:sil=8000:random_seed=1739202971:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 5.74/1.77 % (3503010)First to succeed.
% 5.74/1.77 % (3503010)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3502990"
% 5.74/1.77 % (3503012)Instruction limit reached!
% 5.74/1.77 % (3503012)------------------------------
% 5.74/1.77 % (3503012)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.74/1.77 % (3503012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/1.77 % (3503012)CaDiCaL version: 2.1.3
% 5.74/1.77 % (3503012)Termination reason: Instruction limit
% 5.74/1.77 % (3503012)Termination phase: Saturation
% 5.74/1.77 % (3503012)Time elapsed: 0.075 s
% 5.74/1.77 % (3503012)Peak memory usage: 88 MB
% 5.74/1.77 % (3503012)Instructions burned: 126 (million)
% 5.74/1.77 % (3503011)Instruction limit reached!
% 5.74/1.77 % (3503011)------------------------------
% 5.74/1.77 % (3503011)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.74/1.77 % (3503011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/1.77 % (3503011)CaDiCaL version: 2.1.3
% 5.74/1.77 % (3503011)Termination reason: Instruction limit
% 5.74/1.77 % (3503011)Termination phase: Saturation
% 5.74/1.77 % (3503011)Time elapsed: 0.122 s
% 5.74/1.77 % (3503011)Peak memory usage: 89 MB
% 5.74/1.77 % (3503011)Instructions burned: 221 (million)
% 5.74/1.77 % (3503017)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=1394973918:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 5.74/1.77 % (3503017)Instruction limit reached!
% 5.74/1.77 % (3503017)------------------------------
% 5.74/1.77 % (3503017)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.74/1.77 % (3503017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/1.77 % (3503017)CaDiCaL version: 2.1.3
% 5.74/1.77 % (3503017)Termination reason: Instruction limit
% 5.74/1.77 % (3503017)Termination phase: Saturation
% 5.74/1.77 % (3503017)Time elapsed: 0.033 s
% 5.74/1.77 % (3503017)Peak memory usage: 87 MB
% 5.74/1.77 % (3503017)Instructions burned: 197 (million)
% 5.74/1.77 % (3503018)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=827598807:i=157:gtg=all_2994 on theBenchmark for (2994ds/157Mi)
% 5.74/1.77 % (3503019)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=3539050564:i=3394:sd=4:ss=included:sgt=64_2994 on theBenchmark for (2994ds/3394Mi)
% 5.74/1.77 % (3503021)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=1615403242:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2994 on theBenchmark for (2994ds/106Mi)
% 5.74/1.77 % (3503010)Refutation found. Thanks to Tanya!
% 5.74/1.77 % SZS status Unsatisfiable for theBenchmark
% 5.74/1.77 % SZS output start Proof for theBenchmark
% See solution above
% 5.74/1.77 % (3503010)------------------------------
% 5.74/1.77 % (3503010)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.74/1.77 % (3503010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/1.77 % (3503010)CaDiCaL version: 2.1.3
% 5.74/1.77 % (3503010)Termination reason: Refutation
% 5.74/1.77 % (3503010)Time elapsed: 0.097 s
% 5.74/1.77 % (3503010)Peak memory usage: 90 MB
% 5.74/1.77 % (3503010)Instructions burned: 175 (million)
% 5.74/1.77 % (3503010)------------------------------
% 5.74/1.77 % (3503010)------------------------------
% 5.74/1.77 % (3502990)Success in time 0.732 s
% 5.74/1.77 % Vampire exiting
%------------------------------------------------------------------------------