%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE035+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 : n007.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 11:40:09 AM UTC 2026
% Result : Theorem 5.47s 1.74s
% Output : Refutation 5.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 58 ( 48 unt; 8 def)
% Number of atoms : 85 ( 45 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 39 ( 12 ~; 5 |; 19 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 13 con; 0-2 aty)
% Number of variables : 46 ( 38 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
fof(f19,conjecture,
! [X0,X1,X2,X3] :
( ( test(X3)
& test(X2)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& leq(multiplication(multiplication(X2,X1),c(X3)),zero) )
=> leq(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( test(X3)
& test(X2)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& leq(multiplication(multiplication(X2,X1),c(X3)),zero) )
=> leq(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f27,plain,
? [X0,X1,X2,X3] :
( ~ leq(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero)
& test(X3)
& test(X2)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& leq(multiplication(multiplication(X2,X1),c(X3)),zero) ),
inference(ennf_transformation,[],[f20]) ).
fof(f28,plain,
? [X0,X1,X2,X3] :
( ~ leq(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero)
& test(X3)
& test(X2)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& leq(multiplication(multiplication(X2,X1),c(X3)),zero) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( ( leq(X0,X1)
| addition(X0,X1) != X1 )
& ( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f36,plain,
( ~ leq(multiplication(multiplication(sK3,addition(sK1,sK2)),c(sK4)),zero)
& test(sK4)
& test(sK3)
& leq(multiplication(multiplication(sK3,sK1),c(sK4)),zero)
& leq(multiplication(multiplication(sK3,sK2),c(sK4)),zero) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3),skolemize(X3,sK4)],[f28]) ).
fof(f39,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f40,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f44,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f45,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f48,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f29]) ).
fof(f49,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f61,plain,
leq(multiplication(multiplication(sK3,sK2),c(sK4)),zero),
inference(cnf_transformation,[],[f36]) ).
fof(f62,plain,
leq(multiplication(multiplication(sK3,sK1),c(sK4)),zero),
inference(cnf_transformation,[],[f36]) ).
fof(f65,plain,
~ leq(multiplication(multiplication(sK3,addition(sK1,sK2)),c(sK4)),zero),
inference(cnf_transformation,[],[f36]) ).
fof(f67,definition,
sF5 = addition(sK1,sK2),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f68,plain,
addition(sK1,sK2) = sF5,
inference(reorient_equations,[],[f67]) ).
fof(f69,definition,
sF6 = multiplication(sK3,sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f70,plain,
multiplication(sK3,sF5) = sF6,
inference(reorient_equations,[],[f69]) ).
fof(f71,definition,
sF7 = c(sK4),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f72,plain,
c(sK4) = sF7,
inference(reorient_equations,[],[f71]) ).
fof(f73,definition,
sF8 = multiplication(sF6,sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f74,plain,
multiplication(sF6,sF7) = sF8,
inference(reorient_equations,[],[f73]) ).
fof(f75,plain,
~ leq(sF8,zero),
inference(definition_folding,[],[f65,f74,f72,f70,f68]) ).
fof(f76,definition,
sF9 = multiplication(sK3,sK1),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f77,plain,
multiplication(sK3,sK1) = sF9,
inference(reorient_equations,[],[f76]) ).
fof(f78,definition,
sF10 = multiplication(sF9,sF7),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f79,plain,
multiplication(sF9,sF7) = sF10,
inference(reorient_equations,[],[f78]) ).
fof(f80,plain,
leq(sF10,zero),
inference(definition_folding,[],[f62,f79,f72,f77]) ).
fof(f81,definition,
sF11 = multiplication(sK3,sK2),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f82,plain,
multiplication(sK3,sK2) = sF11,
inference(reorient_equations,[],[f81]) ).
fof(f83,definition,
sF12 = multiplication(sF11,sF7),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f84,plain,
multiplication(sF11,sF7) = sF12,
inference(reorient_equations,[],[f83]) ).
fof(f85,plain,
leq(sF12,zero),
inference(definition_folding,[],[f61,f84,f72,f82]) ).
fof(f86,plain,
zero = addition(sF10,zero),
inference(resolution,[],[f48,f80]) ).
fof(f87,plain,
zero = addition(sF12,zero),
inference(resolution,[],[f48,f85]) ).
fof(f88,plain,
zero = sF12,
inference(forward_demodulation,[],[f87,f39]) ).
fof(f89,plain,
zero = sF10,
inference(forward_demodulation,[],[f86,f39]) ).
fof(f95,plain,
! [X0] : multiplication(sK3,addition(sK1,X0)) = addition(sF9,multiplication(sK3,X0)),
inference(superposition,[],[f44,f77]) ).
fof(f207,plain,
! [X0] : multiplication(addition(X0,sF11),sF7) = addition(multiplication(X0,sF7),sF12),
inference(superposition,[],[f45,f84]) ).
fof(f222,plain,
! [X0] : multiplication(addition(X0,sF11),sF7) = addition(multiplication(X0,sF7),zero),
inference(forward_demodulation,[],[f207,f88]) ).
fof(f227,plain,
! [X0] : multiplication(X0,sF7) = multiplication(addition(X0,sF11),sF7),
inference(forward_demodulation,[],[f222,f39]) ).
fof(f268,plain,
! [X0] :
( X0 != X0
| leq(X0,X0) ),
inference(superposition,[],[f49,f40]) ).
fof(f271,plain,
! [X0] : leq(X0,X0),
inference(trivial_inequality_removal,[],[f268]) ).
fof(f342,plain,
multiplication(sK3,addition(sK1,sK2)) = addition(sF9,sF11),
inference(superposition,[],[f95,f82]) ).
fof(f345,plain,
multiplication(sK3,sF5) = addition(sF9,sF11),
inference(forward_demodulation,[],[f342,f68]) ).
fof(f347,plain,
sF6 = addition(sF9,sF11),
inference(forward_demodulation,[],[f345,f70]) ).
fof(f349,plain,
multiplication(sF6,sF7) = multiplication(sF9,sF7),
inference(superposition,[],[f227,f347]) ).
fof(f360,plain,
multiplication(sF6,sF7) = sF10,
inference(forward_demodulation,[],[f349,f79]) ).
fof(f361,plain,
zero = multiplication(sF6,sF7),
inference(forward_demodulation,[],[f360,f89]) ).
fof(f362,plain,
zero = sF8,
inference(forward_demodulation,[],[f361,f74]) ).
fof(f363,plain,
~ leq(zero,zero),
inference(superposition,[],[f75,f362]) ).
fof(f364,plain,
$false,
inference(forward_subsumption_resolution,[],[f363,f271]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE035+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 13:01:40 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 4.37/1.54 % (1399487)Detected formulas, will run a generic FOF schedule.
% 4.37/1.54 % (1399492)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=2522819819:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.37/1.54 % (1399493)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=1841458716:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.37/1.54 % (1399494)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=240249947:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.37/1.54 % (1399498)dis-21_1_sil=8000:lcm=predicate:random_seed=1639656341: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)
% 4.37/1.54 % (1399496)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3166985095:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.37/1.54 % (1399495)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3629986025:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.37/1.54 % (1399497)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2447850178:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.37/1.54 % (1399498)Refutation not found, incomplete strategy
% 4.37/1.54 % (1399498)------------------------------
% 4.37/1.54 % (1399498)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.37/1.54 % (1399498)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.37/1.54 % (1399498)CaDiCaL version: 2.1.3
% 4.37/1.54 % (1399498)Termination reason: Refutation not found, incomplete strategy
% 4.37/1.54 % (1399498)Time elapsed: 0.002 s
% 4.37/1.54 % (1399498)Peak memory usage: 88 MB
% 4.37/1.54 % (1399498)Instructions burned: 2 (million)
% 4.37/1.54 % (1399495)Instruction limit reached!
% 4.37/1.54 % (1399495)------------------------------
% 4.37/1.54 % (1399495)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.37/1.54 % (1399495)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.37/1.54 % (1399495)CaDiCaL version: 2.1.3
% 4.37/1.54 % (1399495)Termination reason: Instruction limit
% 4.37/1.54 % (1399495)Termination phase: Saturation
% 4.37/1.54 % (1399495)Time elapsed: 0.065 s
% 4.37/1.54 % (1399495)Peak memory usage: 89 MB
% 4.37/1.54 % (1399495)Instructions burned: 110 (million)
% 4.37/1.54 % (1399496)Instruction limit reached!
% 4.37/1.54 % (1399496)------------------------------
% 4.37/1.54 % (1399496)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.37/1.54 % (1399496)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.37/1.54 % (1399496)CaDiCaL version: 2.1.3
% 4.37/1.54 % (1399496)Termination reason: Instruction limit
% 4.37/1.54 % (1399496)Termination phase: Saturation
% 4.37/1.54 % (1399496)Time elapsed: 0.068 s
% 4.37/1.54 % (1399496)Peak memory usage: 89 MB
% 4.37/1.54 % (1399496)Instructions burned: 121 (million)
% 4.37/1.54 % (1399497)Instruction limit reached!
% 4.37/1.54 % (1399497)------------------------------
% 4.37/1.54 % (1399497)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.37/1.54 % (1399497)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.37/1.54 % (1399497)CaDiCaL version: 2.1.3
% 4.37/1.54 % (1399497)Termination reason: Instruction limit
% 4.37/1.54 % (1399497)Termination phase: Saturation
% 4.37/1.54 % (1399497)Time elapsed: 0.081 s
% 4.37/1.54 % (1399497)Peak memory usage: 90 MB
% 4.37/1.54 % (1399497)Instructions burned: 140 (million)
% 4.37/1.54 % (1399506)lrs+10_1_sil=8000:sp=occurrence:random_seed=3727231542:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.37/1.54 % (1399507)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1125792872:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.37/1.54 % (1399508)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3337006324:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.37/1.54 % (1399498)------------------------------
% 4.37/1.54 % (1399498)------------------------------
% 4.37/1.54 % (1399507)Instruction limit reached!
% 4.37/1.54 % (1399507)------------------------------
% 4.37/1.54 % (1399507)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.47/1.74 % (1399507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.74 % (1399507)CaDiCaL version: 2.1.3
% 5.47/1.74 % (1399507)Termination reason: Instruction limit
% 5.47/1.74 % (1399507)Termination phase: Saturation
% 5.47/1.74 % (1399507)Time elapsed: 0.098 s
% 5.47/1.74 % (1399507)Peak memory usage: 90 MB
% 5.47/1.74 % (1399507)Instructions burned: 157 (million)
% 5.47/1.74 % (1399492)First to succeed.
% 5.47/1.74 % (1399506)Instruction limit reached!
% 5.47/1.74 % (1399506)------------------------------
% 5.47/1.74 % (1399506)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.47/1.74 % (1399506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.74 % (1399506)CaDiCaL version: 2.1.3
% 5.47/1.74 % (1399506)Termination reason: Instruction limit
% 5.47/1.74 % (1399506)Termination phase: Saturation
% 5.47/1.74 % (1399506)Time elapsed: 0.178 s
% 5.47/1.74 % (1399506)Peak memory usage: 92 MB
% 5.47/1.74 % (1399506)Instructions burned: 286 (million)
% 5.47/1.74 % (1399492)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1399487"
% 5.47/1.74 % (1399512)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=795488318:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 5.47/1.74 % (1399508)Instruction limit reached!
% 5.47/1.74 % (1399508)------------------------------
% 5.47/1.74 % (1399508)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.47/1.74 % (1399508)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.74 % (1399508)CaDiCaL version: 2.1.3
% 5.47/1.74 % (1399508)Termination reason: Instruction limit
% 5.47/1.74 % (1399508)Termination phase: Saturation
% 5.47/1.74 % (1399508)Time elapsed: 0.198 s
% 5.47/1.74 % (1399508)Peak memory usage: 92 MB
% 5.47/1.74 % (1399508)Instructions burned: 326 (million)
% 5.47/1.74 % (1399513)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1036958950:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 5.47/1.74 % (1399514)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2539802454:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 5.47/1.74 % (1399492)Refutation found. Thanks to Tanya!
% 5.47/1.74 % SZS status Theorem for theBenchmark
% 5.47/1.74 % SZS output start Proof for theBenchmark
% See solution above
% 5.47/1.74 % (1399492)------------------------------
% 5.47/1.74 % (1399492)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.47/1.74 % (1399492)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.47/1.74 % (1399492)CaDiCaL version: 2.1.3
% 5.47/1.74 % (1399492)Termination reason: Refutation
% 5.47/1.74 % (1399492)Time elapsed: 0.417 s
% 5.47/1.74 % (1399492)Peak memory usage: 129 MB
% 5.47/1.74 % (1399492)Instructions burned: 973 (million)
% 5.47/1.74 % (1399492)------------------------------
% 5.47/1.74 % (1399492)------------------------------
% 5.47/1.74 % (1399487)Success in time 0.691 s
% 5.47/1.74 % Vampire exiting
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