%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG077+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 12:35:25 PM UTC 2026
% Result : Theorem 4.19s 1.87s
% Output : Refutation 4.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 54 ( 18 unt; 3 def)
% Number of atoms : 126 ( 31 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 137 ( 65 ~; 52 |; 15 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSZeroSc) ).
fof(f11,axiom,
! [X0,X1] :
( ( aScalar0(X0)
& aScalar0(X1) )
=> aScalar0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulSc) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aScalar0(X0)
& aScalar0(X1)
& aScalar0(X2) )
=> ( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
& sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
& sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
& sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mArith) ).
fof(f48,axiom,
( aScalar0(xE)
& xE = sdtasasdt0(xp,xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1820) ).
fof(f51,axiom,
( aScalar0(xH)
& xH = sdtasdt0(xA,xB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1873) ).
fof(f53,axiom,
( aScalar0(xP)
& xP = sdtasdt0(xE,xH) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1911) ).
fof(f59,conjecture,
sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)) = sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f60,negated_conjecture,
sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),
inference(negated_conjecture,[status(cth)],[f59]) ).
fof(f66,plain,
sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),
inference(flattening,[],[f60]) ).
fof(f75,plain,
! [X0,X1] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X0)
| ~ aScalar0(X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f76,plain,
! [X0,X1] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X0)
| ~ aScalar0(X1) ),
inference(flattening,[],[f75]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
& sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
& sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
& sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
& sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
& sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
& sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(flattening,[],[f79]) ).
fof(f135,plain,
aScalar0(sz0z00),
inference(cnf_transformation,[],[f9]) ).
fof(f137,plain,
! [X0,X1] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X0)
| ~ aScalar0(X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f147,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(cnf_transformation,[],[f80]) ).
fof(f150,plain,
! [X2,X0,X1] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(cnf_transformation,[],[f80]) ).
fof(f201,plain,
aScalar0(xE),
inference(cnf_transformation,[],[f48]) ).
fof(f207,plain,
aScalar0(xH),
inference(cnf_transformation,[],[f51]) ).
fof(f210,plain,
xP = sdtasdt0(xE,xH),
inference(cnf_transformation,[],[f53]) ).
fof(f211,plain,
aScalar0(xP),
inference(cnf_transformation,[],[f53]) ).
fof(f219,plain,
sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),
inference(cnf_transformation,[],[f66]) ).
fof(f224,definition,
( spl2_1
<=> ! [X2] : ~ aScalar0(X2) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f225,plain,
( ! [X2] : ~ aScalar0(X2)
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f224]) ).
fof(f227,definition,
( spl2_2
<=> ! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f228,plain,
( ! [X0,X1] :
( ~ aScalar0(X1)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aScalar0(X0) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f229,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f147,f227,f224]) ).
fof(f239,plain,
sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)) != sdtpldt0(xP,sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),
inference(superposition,[],[f219,f210]) ).
fof(f349,plain,
( ! [X0] :
( ~ aScalar0(X0)
| sdtasdt0(X0,xE) = sdtasdt0(xE,X0) )
| ~ spl2_2 ),
inference(resolution,[],[f228,f201]) ).
fof(f955,definition,
( spl2_39
<=> aScalar0(sdtasdt0(xH,xH)) ),
introduced(definition,[new_symbols(definition,[spl2_39])],[avatar_definition]) ).
fof(f956,plain,
( aScalar0(sdtasdt0(xH,xH))
| ~ spl2_39 ),
inference(avatar_component_clause,[],[f955]) ).
fof(f957,plain,
( ~ aScalar0(sdtasdt0(xH,xH))
| spl2_39 ),
inference(avatar_component_clause,[],[f955]) ).
fof(f968,plain,
( ~ aScalar0(xH)
| ~ aScalar0(xH)
| spl2_39 ),
inference(resolution,[],[f957,f137]) ).
fof(f969,plain,
( ~ aScalar0(xH)
| spl2_39 ),
inference(duplicate_literal_removal,[],[f968]) ).
fof(f970,plain,
( $false
| spl2_39 ),
inference(forward_subsumption_resolution,[],[f969,f207]) ).
fof(f971,plain,
spl2_39,
inference(avatar_contradiction_clause,[],[f970]) ).
fof(f1359,plain,
( sdtasdt0(xE,xH) = sdtasdt0(xH,xE)
| ~ spl2_2 ),
inference(resolution,[],[f349,f207]) ).
fof(f1364,plain,
( xP = sdtasdt0(xH,xE)
| ~ spl2_2 ),
inference(forward_demodulation,[],[f1359,f210]) ).
fof(f1731,plain,
( sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)) != sdtpldt0(xP,sdtpldt0(xP,sdtasdt0(xH,xH)))
| ~ spl2_2 ),
inference(superposition,[],[f239,f1364]) ).
fof(f1762,plain,
( sdtpldt0(xP,sdtpldt0(xP,sdtasdt0(xH,xH))) != sdtpldt0(xP,sdtpldt0(xP,sdtasdt0(xH,xH)))
| ~ aScalar0(xP)
| ~ aScalar0(xP)
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ spl2_2 ),
inference(superposition,[],[f1731,f150]) ).
fof(f1763,plain,
( sdtpldt0(xP,sdtpldt0(xP,sdtasdt0(xH,xH))) != sdtpldt0(xP,sdtpldt0(xP,sdtasdt0(xH,xH)))
| ~ aScalar0(xP)
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ spl2_2 ),
inference(duplicate_literal_removal,[],[f1762]) ).
fof(f1764,plain,
( ~ aScalar0(xP)
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f1763]) ).
fof(f1765,plain,
( ~ aScalar0(sdtasdt0(xH,xH))
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f1764,f211]) ).
fof(f1766,plain,
( $false
| ~ spl2_2
| ~ spl2_39 ),
inference(forward_subsumption_resolution,[],[f1765,f956]) ).
fof(f1767,plain,
( ~ spl2_2
| ~ spl2_39 ),
inference(avatar_contradiction_clause,[],[f1766]) ).
fof(f1768,plain,
( $false
| ~ spl2_1 ),
inference(resolution,[],[f225,f135]) ).
fof(f1835,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f1768]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f229]) ).
cnf(s32,plain,
spl2_39,
inference(sat_conversion,[],[f971]) ).
cnf(s72,plain,
( ~ spl2_2
| ~ spl2_39 ),
inference(sat_conversion,[],[f1767]) ).
cnf(s103,plain,
~ spl2_1,
inference(sat_conversion,[],[f1835]) ).
cnf(s114,plain,
~ spl2_2,
inference(rat,[],[s72,s32]) ).
cnf(s124,plain,
$false,
inference(rat,[],[s1,s114,s103]) ).
fof(f1843,plain,
$false,
inference(avatar_sat_refutation,[],[s124]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG077+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 % Computer : n016.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sun Sep 27 23:14:18 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.46 Running first-order theorem proving
% 0.15/0.46 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
% 4.19/1.87 % (3100182)Detected formulas, will run a generic FOF schedule.
% 4.19/1.87 % (3100192)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3814258683:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.19/1.87 % (3100193)dis-21_1_sil=8000:lcm=predicate:random_seed=2054211591: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)
% 4.19/1.87 % (3100192)First to succeed.
% 4.19/1.87 % (3100192)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3100182"
% 4.19/1.87 % (3100190)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2501311326:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.19/1.87 % (3100188)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=330836566:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.19/1.87 % (3100189)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=13275990:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.19/1.87 % (3100187)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=2842415554:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.19/1.87 % (3100193)Instruction limit reached!
% 4.19/1.87 % (3100193)------------------------------
% 4.19/1.87 % (3100193)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.19/1.87 % (3100193)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.19/1.87 % (3100193)CaDiCaL version: 2.1.3
% 4.19/1.87 % (3100193)Termination reason: Instruction limit
% 4.19/1.87 % (3100193)Termination phase: Saturation
% 4.19/1.87 % (3100193)Time elapsed: 0.093 s
% 4.19/1.87 % (3100193)Peak memory usage: 89 MB
% 4.19/1.87 % (3100193)Instructions burned: 129 (million)
% 4.19/1.87 % (3100191)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2553229762:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.19/1.87 % (3100191)Also succeeded, but the first one will report.
% 4.19/1.87 % (3100190)Also succeeded, but the first one will report.
% 4.19/1.87 % (3100192)Refutation found. Thanks to Tanya!
% 4.19/1.87 % SZS status Theorem for theBenchmark
% 4.19/1.87 % SZS output start Proof for theBenchmark
% See solution above
% 4.19/1.87 % (3100192)------------------------------
% 4.19/1.87 % (3100192)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.19/1.87 % (3100192)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.19/1.87 % (3100192)CaDiCaL version: 2.1.3
% 4.19/1.87 % (3100192)Termination reason: Refutation
% 4.19/1.87 % (3100192)Time elapsed: 0.035 s
% 4.19/1.87 % (3100192)Peak memory usage: 91 MB
% 4.19/1.87 % (3100192)Instructions burned: 59 (million)
% 4.19/1.87 % (3100192)------------------------------
% 4.19/1.87 % (3100192)------------------------------
% 4.19/1.87 % (3100182)Success in time 0.455 s
% 4.19/1.87 % Vampire exiting
%------------------------------------------------------------------------------