%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE025+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 11:40:06 AM UTC 2026
% Result : Theorem 2.66s 1.33s
% Output : Refutation 2.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 38 ( 22 unt; 0 def)
% Number of atoms : 84 ( 53 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 70 ( 24 ~; 18 |; 20 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 55 ( 49 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
fof(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
fof(f14,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_2) ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_3) ).
fof(f19,conjecture,
! [X0,X1,X2] :
( ( test(X1)
& test(X2) )
=> ( multiplication(multiplication(X1,X0),c(X2)) = zero
=> multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0,X1,X2] :
( ( test(X1)
& test(X2) )
=> ( multiplication(multiplication(X1,X0),c(X2)) = zero
=> multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f27,plain,
? [X0,X1,X2] :
( multiplication(X1,X0) != multiplication(multiplication(X1,X0),X2)
& multiplication(multiplication(X1,X0),c(X2)) = zero
& test(X1)
& test(X2) ),
inference(ennf_transformation,[],[f20]) ).
fof(f28,plain,
? [X0,X1,X2] :
( multiplication(X1,X0) != multiplication(multiplication(X1,X0),X2)
& multiplication(multiplication(X1,X0),c(X2)) = zero
& test(X1)
& test(X2) ),
inference(flattening,[],[f27]) ).
fof(f32,plain,
! [X0,X1] :
( ( complement(X1,X0)
| zero != multiplication(X0,X1)
| zero != multiplication(X1,X0)
| addition(X0,X1) != one )
& ( ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one )
| ~ complement(X1,X0) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f33,plain,
! [X0,X1] :
( ( complement(X1,X0)
| zero != multiplication(X0,X1)
| zero != multiplication(X1,X0)
| addition(X0,X1) != one )
& ( ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one )
| ~ complement(X1,X0) ) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( ( ( c(X0) = X1
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(nnf_transformation,[],[f21]) ).
fof(f35,plain,
( multiplication(sK2,sK1) != multiplication(multiplication(sK2,sK1),sK3)
& zero = multiplication(multiplication(sK2,sK1),c(sK3))
& test(sK2)
& test(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f28]) ).
fof(f36,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f38,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f40,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f41,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f43,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f49,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f33]) ).
fof(f53,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f58,plain,
test(sK3),
inference(cnf_transformation,[],[f35]) ).
fof(f60,plain,
zero = multiplication(multiplication(sK2,sK1),c(sK3)),
inference(cnf_transformation,[],[f35]) ).
fof(f61,plain,
multiplication(sK2,sK1) != multiplication(multiplication(sK2,sK1),sK3),
inference(cnf_transformation,[],[f35]) ).
fof(f62,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[],[f53]) ).
fof(f68,plain,
! [X0] :
( one = addition(c(X0),X0)
| ~ test(X0) ),
inference(resolution,[],[f49,f62]) ).
fof(f69,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,c(X0)) ),
inference(forward_demodulation,[],[f68,f36]) ).
fof(f111,plain,
multiplication(sK2,sK1) != multiplication(sK2,multiplication(sK1,sK3)),
inference(superposition,[],[f61,f40]) ).
fof(f132,plain,
! [X0] : multiplication(multiplication(sK2,sK1),addition(X0,c(sK3))) = addition(multiplication(multiplication(sK2,sK1),X0),zero),
inference(superposition,[],[f43,f60]) ).
fof(f144,plain,
! [X0] : multiplication(multiplication(sK2,sK1),X0) = multiplication(multiplication(sK2,sK1),addition(X0,c(sK3))),
inference(forward_demodulation,[],[f132,f38]) ).
fof(f154,plain,
! [X0] : multiplication(multiplication(sK2,sK1),X0) = multiplication(sK2,multiplication(sK1,addition(X0,c(sK3)))),
inference(forward_demodulation,[],[f144,f40]) ).
fof(f160,plain,
! [X0] : multiplication(sK2,multiplication(sK1,addition(X0,c(sK3)))) = multiplication(sK2,multiplication(sK1,X0)),
inference(forward_demodulation,[],[f154,f40]) ).
fof(f373,plain,
one = addition(sK3,c(sK3)),
inference(resolution,[],[f69,f58]) ).
fof(f445,plain,
multiplication(sK2,multiplication(sK1,sK3)) = multiplication(sK2,multiplication(sK1,one)),
inference(superposition,[],[f160,f373]) ).
fof(f447,plain,
multiplication(sK2,sK1) = multiplication(sK2,multiplication(sK1,sK3)),
inference(forward_demodulation,[],[f445,f41]) ).
fof(f448,plain,
$false,
inference(forward_subsumption_resolution,[],[f447,f111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE025+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n010.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 13:03:47 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 2.66/1.33 % (949243)Detected formulas, will run a generic FOF schedule.
% 2.66/1.33 % (949253)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2954334710:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.66/1.33 % (949253)First to succeed.
% 2.66/1.33 % (949253)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-949243"
% 2.66/1.33 % (949252)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1179168351:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.66/1.33 % (949251)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3608437787:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.66/1.33 % (949254)dis-21_1_sil=8000:lcm=predicate:random_seed=4187528001: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)
% 2.66/1.33 % (949248)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=319175003:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.66/1.33 % (949250)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=1123172737:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.66/1.33 % (949249)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=3373374986:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.66/1.33 % (949254)Refutation not found, incomplete strategy
% 2.66/1.33 % (949254)------------------------------
% 2.66/1.33 % (949254)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.33 % (949254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.33 % (949254)CaDiCaL version: 2.1.3
% 2.66/1.33 % (949254)Termination reason: Refutation not found, incomplete strategy
% 2.66/1.33 % (949254)Time elapsed: 0.002 s
% 2.66/1.33 % (949254)Peak memory usage: 88 MB
% 2.66/1.33 % (949254)Instructions burned: 2 (million)
% 2.66/1.33 % (949251)Instruction limit reached!
% 2.66/1.33 % (949251)------------------------------
% 2.66/1.33 % (949251)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.33 % (949251)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.33 % (949251)CaDiCaL version: 2.1.3
% 2.66/1.33 % (949251)Termination reason: Instruction limit
% 2.66/1.33 % (949251)Termination phase: Saturation
% 2.66/1.33 % (949251)Time elapsed: 0.061 s
% 2.66/1.33 % (949251)Peak memory usage: 90 MB
% 2.66/1.33 % (949251)Instructions burned: 109 (million)
% 2.66/1.33 % (949252)Instruction limit reached!
% 2.66/1.33 % (949252)------------------------------
% 2.66/1.33 % (949252)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.33 % (949252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.33 % (949252)CaDiCaL version: 2.1.3
% 2.66/1.33 % (949252)Termination reason: Instruction limit
% 2.66/1.33 % (949252)Termination phase: Saturation
% 2.66/1.33 % (949252)Time elapsed: 0.071 s
% 2.66/1.33 % (949252)Peak memory usage: 89 MB
% 2.66/1.33 % (949252)Instructions burned: 119 (million)
% 2.66/1.33 % (949253)Refutation found. Thanks to Tanya!
% 2.66/1.33 % SZS status Theorem for theBenchmark
% 2.66/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 2.66/1.33 % (949253)------------------------------
% 2.66/1.33 % (949253)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.33 % (949253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.33 % (949253)CaDiCaL version: 2.1.3
% 2.66/1.33 % (949253)Termination reason: Refutation
% 2.66/1.33 % (949253)Time elapsed: 0.007 s
% 2.66/1.33 % (949253)Peak memory usage: 89 MB
% 2.66/1.33 % (949253)Instructions burned: 17 (million)
% 2.66/1.33 % (949253)------------------------------
% 2.66/1.33 % (949253)------------------------------
% 2.66/1.33 % (949243)Success in time 0.287 s
% 2.66/1.33 % Vampire exiting
%------------------------------------------------------------------------------