%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM478+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 : n004.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 12:15:22 PM UTC 2026
% Result : Theorem 2.62s 1.32s
% Output : Refutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 16 unt; 0 def)
% Number of atoms : 141 ( 67 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 168 ( 76 ~; 63 |; 21 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 40 ( 39 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(f10,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(f15,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 != sz00
=> ! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtasdt0(X0,X1) = sdtasdt0(X0,X2)
| sdtasdt0(X1,X0) = sdtasdt0(X2,X0) )
=> X1 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).
fof(f36,axiom,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1524) ).
fof(f37,axiom,
( xl != sz00
& ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xl,X0) )
& doDivides0(xl,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1524_04) ).
fof(f38,axiom,
aNaturalNumber0(xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1553) ).
fof(f39,conjecture,
( ( aNaturalNumber0(sdtsldt0(xm,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl)) )
=> ( sdtasdt0(xn,xm) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))
| sdtasdt0(xn,sdtsldt0(xm,xl)) = sdtsldt0(sdtasdt0(xn,xm),xl) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f40,negated_conjecture,
~ ( ( aNaturalNumber0(sdtsldt0(xm,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl)) )
=> ( sdtasdt0(xn,xm) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))
| sdtasdt0(xn,sdtsldt0(xm,xl)) = sdtsldt0(sdtasdt0(xn,xm),xl) ) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f42,plain,
( sdtasdt0(xn,xm) != sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))
& sdtasdt0(xn,sdtsldt0(xm,xl)) != sdtsldt0(sdtasdt0(xn,xm),xl)
& aNaturalNumber0(sdtsldt0(xm,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl)) ),
inference(ennf_transformation,[],[f40]) ).
fof(f43,plain,
( sdtasdt0(xn,xm) != sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))
& sdtasdt0(xn,sdtsldt0(xm,xl)) != sdtsldt0(sdtasdt0(xn,xm),xl)
& aNaturalNumber0(sdtsldt0(xm,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl)) ),
inference(flattening,[],[f42]) ).
fof(f46,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f47,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f46]) ).
fof(f49,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f10]) ).
fof(f50,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f52,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f51]) ).
fof(f95,plain,
( xl != sz00
& aNaturalNumber0(sK0)
& xm = sdtasdt0(xl,sK0)
& doDivides0(xl,xm) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f37]) ).
fof(f104,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f36]) ).
fof(f105,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f36]) ).
fof(f107,plain,
xm = sdtasdt0(xl,sK0),
inference(cnf_transformation,[],[f95]) ).
fof(f108,plain,
aNaturalNumber0(sK0),
inference(cnf_transformation,[],[f95]) ).
fof(f109,plain,
sz00 != xl,
inference(cnf_transformation,[],[f95]) ).
fof(f110,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f38]) ).
fof(f111,plain,
xm = sdtasdt0(xl,sdtsldt0(xm,xl)),
inference(cnf_transformation,[],[f43]) ).
fof(f112,plain,
aNaturalNumber0(sdtsldt0(xm,xl)),
inference(cnf_transformation,[],[f43]) ).
fof(f114,plain,
sdtasdt0(xn,xm) != sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))),
inference(cnf_transformation,[],[f43]) ).
fof(f117,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f121,plain,
! [X2,X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f50]) ).
fof(f122,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f507,plain,
! [X0] :
( sdtasdt0(xm,X0) = sdtasdt0(xl,sdtasdt0(sK0,X0))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sK0)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[],[f121,f107]) ).
fof(f550,plain,
! [X0] :
( sdtasdt0(xm,X0) = sdtasdt0(xl,sdtasdt0(sK0,X0))
| ~ aNaturalNumber0(sK0)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f507,f105]) ).
fof(f561,plain,
! [X0] :
( sdtasdt0(xm,X0) = sdtasdt0(xl,sdtasdt0(sK0,X0))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f550,f108]) ).
fof(f815,plain,
! [X0] :
( xm != sdtasdt0(xl,X0)
| sdtsldt0(xm,xl) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| sz00 = xl
| ~ aNaturalNumber0(xl) ),
inference(superposition,[],[f117,f111]) ).
fof(f835,plain,
! [X0] :
( xm != sdtasdt0(xl,X0)
| sdtsldt0(xm,xl) = X0
| ~ aNaturalNumber0(X0)
| sz00 = xl
| ~ aNaturalNumber0(xl) ),
inference(forward_subsumption_resolution,[],[f815,f112]) ).
fof(f853,plain,
! [X0] :
( xm != sdtasdt0(xl,X0)
| sdtsldt0(xm,xl) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xl) ),
inference(forward_subsumption_resolution,[],[f835,f109]) ).
fof(f864,plain,
! [X0] :
( xm != sdtasdt0(xl,X0)
| sdtsldt0(xm,xl) = X0
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f853,f105]) ).
fof(f1628,plain,
( xm != xm
| sdtsldt0(xm,xl) = sK0
| ~ aNaturalNumber0(sK0) ),
inference(superposition,[],[f864,f107]) ).
fof(f1636,plain,
( sdtsldt0(xm,xl) = sK0
| ~ aNaturalNumber0(sK0) ),
inference(trivial_inequality_removal,[],[f1628]) ).
fof(f1642,plain,
sdtsldt0(xm,xl) = sK0,
inference(forward_subsumption_resolution,[],[f1636,f108]) ).
fof(f1652,plain,
sdtasdt0(xn,xm) != sdtasdt0(xl,sdtasdt0(xn,sK0)),
inference(superposition,[],[f114,f1642]) ).
fof(f1669,plain,
( sdtasdt0(xn,xm) != sdtasdt0(xl,sdtasdt0(sK0,xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sK0) ),
inference(superposition,[],[f1652,f122]) ).
fof(f1670,plain,
( sdtasdt0(xn,xm) != sdtasdt0(xl,sdtasdt0(sK0,xn))
| ~ aNaturalNumber0(sK0) ),
inference(forward_subsumption_resolution,[],[f1669,f110]) ).
fof(f1672,plain,
sdtasdt0(xn,xm) != sdtasdt0(xl,sdtasdt0(sK0,xn)),
inference(forward_subsumption_resolution,[],[f1670,f108]) ).
fof(f2545,plain,
( sdtasdt0(xn,xm) != sdtasdt0(xm,xn)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[],[f1672,f561]) ).
fof(f2593,plain,
sdtasdt0(xn,xm) != sdtasdt0(xm,xn),
inference(forward_subsumption_resolution,[],[f2545,f110]) ).
fof(f2607,plain,
( sdtasdt0(xn,xm) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[],[f2593,f122]) ).
fof(f2608,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(trivial_inequality_removal,[],[f2607]) ).
fof(f2610,plain,
~ aNaturalNumber0(xn),
inference(forward_subsumption_resolution,[],[f2608,f104]) ).
fof(f2612,plain,
$false,
inference(forward_subsumption_resolution,[],[f2610,f110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM478+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n004.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 20:05:53 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 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
% 2.62/1.32 % (3846718)Detected formulas, will run a generic FOF schedule.
% 2.62/1.32 % (3846727)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2682105532:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.62/1.32 % (3846727)First to succeed.
% 2.62/1.32 % (3846727)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3846718"
% 2.62/1.32 % (3846728)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=424688911:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.62/1.32 % (3846726)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4215342132:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.62/1.32 % (3846723)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=439823380:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.62/1.32 % (3846724)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=3351099895:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.62/1.32 % (3846725)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=3854554392:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.62/1.32 % (3846729)dis-21_1_sil=8000:lcm=predicate:random_seed=2162310374: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)
% 2.62/1.32 % (3846726)Also succeeded, but the first one will report.
% 2.62/1.32 % (3846729)Instruction limit reached!
% 2.62/1.32 % (3846729)------------------------------
% 2.62/1.32 % (3846729)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.32 % (3846729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.32 % (3846729)CaDiCaL version: 2.1.3
% 2.62/1.32 % (3846729)Termination reason: Instruction limit
% 2.62/1.32 % (3846729)Termination phase: Saturation
% 2.62/1.32 % (3846729)Time elapsed: 0.079 s
% 2.62/1.32 % (3846729)Peak memory usage: 91 MB
% 2.62/1.32 % (3846729)Instructions burned: 131 (million)
% 2.62/1.32 % (3846728)Instruction limit reached!
% 2.62/1.32 % (3846728)------------------------------
% 2.62/1.32 % (3846728)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.32 % (3846728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.32 % (3846728)CaDiCaL version: 2.1.3
% 2.62/1.32 % (3846728)Termination reason: Instruction limit
% 2.62/1.32 % (3846728)Termination phase: Saturation
% 2.62/1.32 % (3846728)Time elapsed: 0.099 s
% 2.62/1.32 % (3846728)Peak memory usage: 90 MB
% 2.62/1.32 % (3846728)Instructions burned: 139 (million)
% 2.62/1.32 % (3846727)Refutation found. Thanks to Tanya!
% 2.62/1.32 % SZS status Theorem for theBenchmark
% 2.62/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.62/1.32 % (3846727)------------------------------
% 2.62/1.32 % (3846727)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.32 % (3846727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.32 % (3846727)CaDiCaL version: 2.1.3
% 2.62/1.32 % (3846727)Termination reason: Refutation
% 2.62/1.32 % (3846727)Time elapsed: 0.027 s
% 2.62/1.32 % (3846727)Peak memory usage: 89 MB
% 2.62/1.32 % (3846727)Instructions burned: 84 (million)
% 2.62/1.32 % (3846727)------------------------------
% 2.62/1.32 % (3846727)------------------------------
% 2.62/1.32 % (3846718)Success in time 0.289 s
% 2.62/1.32 % Vampire exiting
%------------------------------------------------------------------------------