%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW204+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 01:29:50 PM UTC 2026
% Result : Theorem 0.21s 1.40s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 10 unt; 0 def)
% Number of atoms : 24 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 12 ~; 7 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 15 ( 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X0))),v_r)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms) ).
fof(f9,axiom,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X1))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__trans) ).
fof(f15,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__0960_A_060_061_Acmod_A_Is_A0_J_096) ).
fof(f1264,conjecture,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f1265,negated_conjecture,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
inference(negated_conjecture,[status(cth)],[f1264]) ).
fof(f1272,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
inference(flattening,[],[f1265]) ).
fof(f1278,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X1)) ),
inference(ennf_transformation,[],[f9]) ).
fof(f1279,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X1)) ),
inference(flattening,[],[f1278]) ).
fof(f2704,plain,
! [X0] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,X0))),v_r)),
inference(cnf_transformation,[],[f4]) ).
fof(f2709,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2),X1)) ),
inference(cnf_transformation,[],[f1279]) ).
fof(f2718,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(cnf_transformation,[],[f15]) ).
fof(f4372,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
inference(cnf_transformation,[],[f1272]) ).
fof(f4596,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),X0))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0),v_r)) ),
inference(resolution,[],[f2709,f4372]) ).
fof(f4742,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r)),
inference(resolution,[],[f2718,f4596]) ).
fof(f4753,plain,
$false,
inference(forward_subsumption_resolution,[],[f4742,f2704]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW204+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n008.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 13:18:55 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running first-order theorem proving
% 0.09/0.24 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
% 0.21/1.40 % (2243950)Detected formulas, will run a generic FOF schedule.
% 0.21/1.40 % (2243959)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1979982627:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.21/1.40 % (2243959)Instruction limit reached!
% 0.21/1.40 % (2243959)------------------------------
% 0.21/1.40 % (2243959)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.40 % (2243959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.40 % (2243959)CaDiCaL version: 2.1.3
% 0.21/1.40 % (2243959)Termination reason: Instruction limit
% 0.21/1.40 % (2243959)Termination phase: Saturation
% 0.21/1.40 % (2243959)Time elapsed: 0.037 s
% 0.21/1.40 % (2243959)Peak memory usage: 90 MB
% 0.21/1.40 % (2243959)Instructions burned: 120 (million)
% 0.21/1.40 % (2243960)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2036785991:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.21/1.40 % (2243957)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=1418305765:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.21/1.40 % (2243955)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=3833737001:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.21/1.40 % (2243961)dis-21_1_sil=8000:lcm=predicate:random_seed=1840125747: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)
% 0.21/1.40 % (2243958)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3490506658:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.21/1.40 % (2243956)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=2070962066:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.21/1.40 % (2243958)Instruction limit reached!
% 0.21/1.40 % (2243958)------------------------------
% 0.21/1.40 % (2243958)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.40 % (2243958)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.40 % (2243958)CaDiCaL version: 2.1.3
% 0.21/1.40 % (2243958)Termination reason: Instruction limit
% 0.21/1.40 % (2243958)Termination phase: Saturation
% 0.21/1.40 % (2243958)Time elapsed: 0.047 s
% 0.21/1.40 % (2243958)Peak memory usage: 89 MB
% 0.21/1.40 % (2243958)Instructions burned: 110 (million)
% 0.21/1.40 % (2243961)Instruction limit reached!
% 0.21/1.40 % (2243961)------------------------------
% 0.21/1.40 % (2243961)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.40 % (2243961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.40 % (2243961)CaDiCaL version: 2.1.3
% 0.21/1.40 % (2243961)Termination reason: Instruction limit
% 0.21/1.40 % (2243961)Termination phase: Saturation
% 0.21/1.40 % (2243961)Time elapsed: 0.061 s
% 0.21/1.40 % (2243961)Peak memory usage: 90 MB
% 0.21/1.40 % (2243961)Instructions burned: 129 (million)
% 0.21/1.40 % (2243960)First to succeed.
% 0.21/1.40 % (2243960)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2243950"
% 0.21/1.40 % (2243963)lrs+10_1_sil=8000:sp=occurrence:random_seed=560599021:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.21/1.40 % (2243970)lrs+10_1_sil=32000:urr=on:br=off:random_seed=913556924:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 0.21/1.40 % (2243963)Instruction limit reached!
% 0.21/1.40 % (2243963)------------------------------
% 0.21/1.40 % (2243963)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.40 % (2243963)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.40 % (2243963)CaDiCaL version: 2.1.3
% 0.21/1.40 % (2243963)Termination reason: Instruction limit
% 0.21/1.40 % (2243963)Termination phase: Saturation
% 0.21/1.40 % (2243963)Time elapsed: 0.095 s
% 0.21/1.40 % (2243963)Peak memory usage: 92 MB
% 0.21/1.40 % (2243963)Instructions burned: 286 (million)
% 0.21/1.40 % (2243970)Refutation not found, incomplete strategy
% 0.21/1.40 % (2243970)------------------------------
% 0.21/1.40 % (2243970)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.40 % (2243970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.40 % (2243970)CaDiCaL version: 2.1.3
% 0.21/1.40 % (2243970)Termination reason: Refutation not found, incomplete strategy
% 0.21/1.40 % (2243970)Time elapsed: 0.013 s
% 0.21/1.40 % (2243970)Peak memory usage: 89 MB
% 0.21/1.40 % (2243970)Instructions burned: 25 (million)
% 0.21/1.40 % (2243971)lrs+1011_1_sil=32000:sp=occurrence:random_seed=442252472:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 0.21/1.40 % (2243974)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=350542406:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 0.21/1.40 % (2243974)Also succeeded, but the first one will report.
% 0.21/1.40 % (2243960)Refutation found. Thanks to Tanya!
% 0.21/1.40 % SZS status Theorem for theBenchmark
% 0.21/1.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/1.40 % (2243960)------------------------------
% 0.21/1.40 % (2243960)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.40 % (2243960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.40 % (2243960)CaDiCaL version: 2.1.3
% 0.21/1.40 % (2243960)Termination reason: Refutation
% 0.21/1.40 % (2243960)Time elapsed: 0.064 s
% 0.21/1.40 % (2243960)Peak memory usage: 91 MB
% 0.21/1.40 % (2243960)Instructions burned: 130 (million)
% 0.21/1.40 % (2243960)------------------------------
% 0.21/1.40 % (2243960)------------------------------
% 0.21/1.40 % (2243950)Success in time 0.531 s
% 0.21/1.40 % Vampire exiting
%------------------------------------------------------------------------------