%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW225+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 : n014.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 01:29:53 PM UTC 2026
% Result : Theorem 0.20s 1.60s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 8 unt; 0 def)
% Number of atoms : 24 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 20 ( 10 ~; 6 |; 2 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 12 ( 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096N1_A_L_AN2_A_060_061_Af_A_IN1_A_L_AN2_J_096) ).
fof(f23,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
fof(f69,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__le__iff) ).
fof(f1269,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f1270,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(negated_conjecture,[status(cth)],[f1269]) ).
fof(f1281,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(flattening,[],[f1270]) ).
fof(f2344,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0)) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f2363,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)) ) ),
inference(nnf_transformation,[],[f69]) ).
fof(f2745,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),
inference(cnf_transformation,[],[f3]) ).
fof(f2768,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2344]) ).
fof(f2830,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2363]) ).
fof(f4462,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(cnf_transformation,[],[f1281]) ).
fof(f6198,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),
inference(unit_resulting_resolution,[],[f2830,f4462]) ).
fof(f6240,plain,
$false,
inference(unit_resulting_resolution,[],[f2768,f2745,f6198]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW225+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n014.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 13:18:46 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 0.20/1.60 % (1772825)Detected formulas, will run a generic FOF schedule.
% 0.20/1.60 % (1772833)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=110381907:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.20/1.60 % (1772833)Instruction limit reached!
% 0.20/1.60 % (1772833)------------------------------
% 0.20/1.60 % (1772833)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.60 % (1772833)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.60 % (1772833)CaDiCaL version: 2.1.3
% 0.20/1.60 % (1772833)Termination reason: Instruction limit
% 0.20/1.60 % (1772833)Termination phase: Saturation
% 0.20/1.60 % (1772833)Time elapsed: 0.034 s
% 0.20/1.60 % (1772833)Peak memory usage: 90 MB
% 0.20/1.60 % (1772833)Instructions burned: 110 (million)
% 0.20/1.60 % (1772835)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4108532:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.20/1.60 % (1772832)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=1731891218:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.20/1.60 % (1772831)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=3591525856:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.20/1.60 % (1772830)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=3264459284:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.20/1.60 % (1772834)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1194012024:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.20/1.60 % (1772836)dis-21_1_sil=8000:lcm=predicate:random_seed=2876963621: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)
% 0.20/1.60 % (1772834)Instruction limit reached!
% 0.20/1.60 % (1772834)------------------------------
% 0.20/1.60 % (1772834)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.60 % (1772834)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.60 % (1772834)CaDiCaL version: 2.1.3
% 0.20/1.60 % (1772834)Termination reason: Instruction limit
% 0.20/1.60 % (1772834)Termination phase: Saturation
% 0.20/1.60 % (1772834)Time elapsed: 0.065 s
% 0.20/1.60 % (1772834)Peak memory usage: 89 MB
% 0.20/1.60 % (1772834)Instructions burned: 121 (million)
% 0.20/1.60 % (1772836)Instruction limit reached!
% 0.20/1.60 % (1772836)------------------------------
% 0.20/1.60 % (1772836)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.60 % (1772836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.60 % (1772836)CaDiCaL version: 2.1.3
% 0.20/1.60 % (1772836)Termination reason: Instruction limit
% 0.20/1.60 % (1772836)Termination phase: Saturation
% 0.20/1.60 % (1772836)Time elapsed: 0.067 s
% 0.20/1.60 % (1772836)Peak memory usage: 91 MB
% 0.20/1.60 % (1772836)Instructions burned: 130 (million)
% 0.20/1.60 % (1772835)Instruction limit reached!
% 0.20/1.60 % (1772835)------------------------------
% 0.20/1.60 % (1772835)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.60 % (1772835)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.60 % (1772835)CaDiCaL version: 2.1.3
% 0.20/1.60 % (1772835)Termination reason: Instruction limit
% 0.20/1.60 % (1772835)Termination phase: Saturation
% 0.20/1.60 % (1772835)Time elapsed: 0.077 s
% 0.20/1.60 % (1772835)Peak memory usage: 91 MB
% 0.20/1.60 % (1772835)Instructions burned: 139 (million)
% 0.20/1.60 % (1772842)lrs+10_1_sil=8000:sp=occurrence:random_seed=795029748:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 0.20/1.60 % (1772842)Instruction limit reached!
% 0.20/1.60 % (1772842)------------------------------
% 0.20/1.60 % (1772842)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.60 % (1772842)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.60 % (1772842)CaDiCaL version: 2.1.3
% 0.20/1.60 % (1772842)Termination reason: Instruction limit
% 0.20/1.60 % (1772842)Termination phase: Saturation
% 0.20/1.60 % (1772842)Time elapsed: 0.099 s
% 0.20/1.60 % (1772842)Peak memory usage: 92 MB
% 0.20/1.60 % (1772842)Instructions burned: 286 (million)
% 0.20/1.60 % (1772846)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3549809331:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 0.20/1.60 % (1772845)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3356862224:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 0.20/1.60 % (1772847)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=401417875:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 0.20/1.60 % (1772849)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2023500169:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 0.20/1.60 % (1772847)First to succeed.
% 0.20/1.60 % (1772847)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1772825"
% 0.20/1.60 % (1772849)Also succeeded, but the first one will report.
% 0.20/1.60 % (1772845)Instruction limit reached!
% 0.20/1.60 % (1772845)------------------------------
% 0.20/1.60 % (1772845)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.60 % (1772845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.60 % (1772845)CaDiCaL version: 2.1.3
% 0.20/1.60 % (1772845)Termination reason: Instruction limit
% 0.20/1.60 % (1772845)Termination phase: Saturation
% 0.20/1.60 % (1772845)Time elapsed: 0.092 s
% 0.20/1.60 % (1772845)Peak memory usage: 90 MB
% 0.20/1.60 % (1772845)Instructions burned: 159 (million)
% 0.20/1.60 % (1772846)Instruction limit reached!
% 0.20/1.60 % (1772846)------------------------------
% 0.20/1.60 % (1772846)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.60 % (1772846)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.60 % (1772846)CaDiCaL version: 2.1.3
% 0.20/1.60 % (1772846)Termination reason: Instruction limit
% 0.20/1.60 % (1772846)Termination phase: Saturation
% 0.20/1.60 % (1772846)Time elapsed: 0.198 s
% 0.20/1.60 % (1772846)Peak memory usage: 92 MB
% 0.20/1.60 % (1772846)Instructions burned: 326 (million)
% 0.20/1.60 % (1772854)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1877420816:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 0.20/1.60 % (1772855)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3414167530:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 0.20/1.60 % (1772847)Refutation found. Thanks to Tanya!
% 0.20/1.60 % SZS status Theorem for theBenchmark
% 0.20/1.60 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/1.60 % (1772847)------------------------------
% 0.20/1.60 % (1772847)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.60 % (1772847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.60 % (1772847)CaDiCaL version: 2.1.3
% 0.20/1.60 % (1772847)Termination reason: Refutation
% 0.20/1.60 % (1772847)Time elapsed: 0.079 s
% 0.20/1.60 % (1772847)Peak memory usage: 91 MB
% 0.20/1.60 % (1772847)Instructions burned: 138 (million)
% 0.20/1.60 % (1772847)------------------------------
% 0.20/1.60 % (1772847)------------------------------
% 0.20/1.60 % (1772825)Success in time 0.737 s
% 0.20/1.60 % Vampire exiting
%------------------------------------------------------------------------------