%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW263+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 : n001.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 01:29:58 PM UTC 2026
% Result : Theorem 4.74s 1.44s
% Output : Refutation 4.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 10 unt; 0 def)
% Number of atoms : 22 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 10 ~; 6 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-3 aty)
% Number of variables : 12 ( 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__0960_A_060_At_A_094_Ak_096) ).
fof(f7,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096t_A_K_A_Icmod_Aw_A_094_A_Ik_A_L_A1_J_A_K_Am_J_A_060_A1_096) ).
fof(f288,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__less__mono2) ).
fof(f1288,conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f1289,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(negated_conjecture,[status(cth)],[f1288]) ).
fof(f1292,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(flattening,[],[f1289]) ).
fof(f1626,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X0))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(ennf_transformation,[],[f288]) ).
fof(f1627,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X0))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(flattening,[],[f1626]) ).
fof(f2754,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)),
inference(cnf_transformation,[],[f6]) ).
fof(f2755,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f7]) ).
fof(f3153,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X0))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(cnf_transformation,[],[f1627]) ).
fof(f4400,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(cnf_transformation,[],[f1292]) ).
fof(f6347,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(unit_resulting_resolution,[],[f3153,f2754,f4400]) ).
fof(f6767,plain,
$false,
inference(forward_subsumption_resolution,[],[f2755,f6347]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW263+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.26 % Computer : n001.cluster.edu
% 0.08/0.26 % Model : x86_64 x86_64
% 0.08/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.26 % Memory : 8046.5625MB
% 0.08/0.26 % OS : Linux 6.8.0-71-generic
% 0.08/0.26 % CPULimit : 300
% 0.08/0.26 % WCLimit : 300
% 0.08/0.26 % DateTime : Mon Sep 28 13:31:48 UTC 2026
% 0.08/0.26 % CPUTime :
% 0.08/0.26 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.33 Running first-order theorem proving
% 0.24/0.33 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
% 4.17/1.24 % (353553)Detected formulas, will run a generic FOF schedule.
% 4.17/1.24 % (353559)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=4018738145:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.17/1.24 % (353564)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4234250988:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.17/1.24 % (353565)dis-21_1_sil=8000:lcm=predicate:random_seed=3677354495: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)
% 4.17/1.24 % (353560)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=2141490495:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.17/1.24 % (353562)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=524090663:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.17/1.24 % (353563)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=276232472:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.17/1.24 % (353561)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=1737715498:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.17/1.24 % (353562)Instruction limit reached!
% 4.17/1.24 % (353562)------------------------------
% 4.17/1.24 % (353562)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.24 % (353562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.24 % (353562)CaDiCaL version: 2.1.3
% 4.17/1.24 % (353562)Termination reason: Instruction limit
% 4.17/1.24 % (353562)Termination phase: Saturation
% 4.17/1.24 % (353562)Time elapsed: 0.060 s
% 4.17/1.24 % (353562)Peak memory usage: 90 MB
% 4.17/1.24 % (353562)Instructions burned: 110 (million)
% 4.17/1.24 % (353565)Instruction limit reached!
% 4.17/1.24 % (353565)------------------------------
% 4.17/1.24 % (353565)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.24 % (353565)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.24 % (353565)CaDiCaL version: 2.1.3
% 4.17/1.24 % (353565)Termination reason: Instruction limit
% 4.17/1.24 % (353565)Termination phase: Saturation
% 4.17/1.24 % (353565)Time elapsed: 0.067 s
% 4.17/1.24 % (353565)Peak memory usage: 91 MB
% 4.17/1.24 % (353565)Instructions burned: 130 (million)
% 4.17/1.24 % (353563)Instruction limit reached!
% 4.17/1.24 % (353563)------------------------------
% 4.17/1.24 % (353563)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.24 % (353563)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.24 % (353563)CaDiCaL version: 2.1.3
% 4.17/1.24 % (353563)Termination reason: Instruction limit
% 4.17/1.24 % (353563)Termination phase: Saturation
% 4.17/1.24 % (353563)Time elapsed: 0.067 s
% 4.17/1.24 % (353563)Peak memory usage: 89 MB
% 4.17/1.24 % (353563)Instructions burned: 121 (million)
% 4.17/1.24 % (353564)Instruction limit reached!
% 4.17/1.24 % (353564)------------------------------
% 4.17/1.24 % (353564)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.24 % (353564)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.24 % (353564)CaDiCaL version: 2.1.3
% 4.17/1.24 % (353564)Termination reason: Instruction limit
% 4.17/1.24 % (353564)Termination phase: Saturation
% 4.17/1.24 % (353564)Time elapsed: 0.088 s
% 4.17/1.24 % (353564)Peak memory usage: 90 MB
% 4.17/1.24 % (353564)Instructions burned: 141 (million)
% 4.17/1.24 % (353573)lrs+10_1_sil=8000:sp=occurrence:random_seed=3579133822:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.17/1.24 % (353576)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=2062168584:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.17/1.24 % (353575)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3603987577:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.17/1.24 % (353574)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2047218878:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.17/1.24 % (353576)First to succeed.
% 4.17/1.24 % (353576)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-353553"
% 4.74/1.44 % (353574)Instruction limit reached!
% 4.74/1.44 % (353574)------------------------------
% 4.74/1.44 % (353574)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.74/1.44 % (353574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.74/1.44 % (353574)CaDiCaL version: 2.1.3
% 4.74/1.44 % (353574)Termination reason: Instruction limit
% 4.74/1.44 % (353574)Termination phase: Saturation
% 4.74/1.44 % (353574)Time elapsed: 0.088 s
% 4.74/1.44 % (353574)Peak memory usage: 90 MB
% 4.74/1.44 % (353574)Instructions burned: 158 (million)
% 4.74/1.44 % (353573)Instruction limit reached!
% 4.74/1.44 % (353573)------------------------------
% 4.74/1.44 % (353573)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.74/1.44 % (353573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.74/1.44 % (353573)CaDiCaL version: 2.1.3
% 4.74/1.44 % (353573)Termination reason: Instruction limit
% 4.74/1.44 % (353573)Termination phase: Saturation
% 4.74/1.44 % (353573)Time elapsed: 0.184 s
% 4.74/1.44 % (353573)Peak memory usage: 92 MB
% 4.74/1.44 % (353573)Instructions burned: 286 (million)
% 4.74/1.44 % (353576)Refutation found. Thanks to Tanya!
% 4.74/1.44 % SZS status Theorem for theBenchmark
% 4.74/1.44 % SZS output start Proof for theBenchmark
% See solution above
% 4.74/1.44 % (353576)------------------------------
% 4.74/1.44 % (353576)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.74/1.44 % (353576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.74/1.44 % (353576)CaDiCaL version: 2.1.3
% 4.74/1.44 % (353576)Termination reason: Refutation
% 4.74/1.44 % (353576)Time elapsed: 0.049 s
% 4.74/1.44 % (353576)Peak memory usage: 92 MB
% 4.74/1.44 % (353576)Instructions burned: 162 (million)
% 4.74/1.44 % (353576)------------------------------
% 4.74/1.44 % (353576)------------------------------
% 4.74/1.44 % (353553)Success in time 0.599 s
% 4.74/1.44 % Vampire exiting
%------------------------------------------------------------------------------