%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL745-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 11:56:25 AM UTC 2026
% Result : Unsatisfiable 0.21s 2.60s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 19 ( 14 unt; 0 def)
% Number of atoms : 26 ( 13 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 10 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 8 con; 0-5 aty)
% Number of variables : 47 ( 47 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f304,axiom,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),X3),X2)
| ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X1 = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
fof(f307,axiom,
! [X2,X0,X1] :
( ~ hBOOL(c_HOL_Oinduct__forall(X0,X2))
| hBOOL(hAPP(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_induct__forall__def_0) ).
fof(f361,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X0),c_HOL_Ozero__class_Ozero(X0)),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).
fof(f572,axiom,
! [X0,X1] : hBOOL(c_List_Olistsp(X0,c_List_Olist_ONil(X1),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).
fof(f621,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n),v_rs,tc_Lambda_OdB,tc_Lambda_OdB)),v_ia))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f637,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(f646,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(f664,axiom,
! [X2,X3,X0,X1,X4,X5] : hAPP(hAPP(c_COMBS(X0,X1,X2,X3),X4),X5) = hAPP(hAPP(X0,X5),hAPP(X4,X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBS__def_0) ).
fof(f666,axiom,
! [X2,X3,X0,X1,X4,X5] : hAPP(hAPP(hAPP(c_COMBB(X0,X1,X2),X3),X4),X5) = hAPP(X3,hAPP(X4,X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).
fof(f786,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : hAPP(hAPP(c_COMBS(hAPP(c_COMBB(X0,X1,X2),X3),X4,X5,X6),X7),X8) = hAPP(X3,hAPP(X8,hAPP(X7,X8))),
inference(superposition,[],[f666,f664]) ).
fof(f1509,plain,
! [X0] : ~ hBOOL(c_HOL_Oinduct__forall(c_InductTermi_OIT,X0)),
inference(unit_resulting_resolution,[],[f307,f621]) ).
fof(f1736,plain,
! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X0) = X0,
inference(unit_resulting_resolution,[],[f361,f646]) ).
fof(f1741,plain,
! [X0,X1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0) != X0
| ~ class_OrderedGroup_Ocancel__semigroup__add(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 ),
inference(superposition,[],[f304,f1736]) ).
fof(f1751,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] : hAPP(X4,hAPP(X0,X0)) = hAPP(hAPP(c_COMBS(hAPP(c_COMBB(X1,X2,X3),X4),X5,X6,X7),hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))),X0),
inference(superposition,[],[f786,f1736]) ).
fof(f1762,plain,
! [X0,X1] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0) != X0
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 ),
inference(forward_subsumption_resolution,[],[f1741,f637]) ).
fof(f1911,plain,
! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = X0,
inference(unit_resulting_resolution,[],[f1762,f1751]) ).
fof(f2299,plain,
hBOOL(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(superposition,[],[f572,f1911]) ).
fof(f2302,plain,
~ hBOOL(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(superposition,[],[f1509,f1911]) ).
fof(f2312,plain,
$false,
inference(forward_subsumption_resolution,[],[f2299,f2302]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL745-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 % Computer : n020.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sun Sep 27 16:43:49 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.47 Running first-order theorem proving
% 0.14/0.47 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
% 9.73/2.36 % (3596154)Input is clausal, will run a generic CNF schedule.
% 9.73/2.36 % (3596160)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3001214450:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 9.73/2.36 % (3596161)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1871430749:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 9.73/2.36 % (3596164)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4005962954:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 9.73/2.36 % (3596165)dis-21_1_sil=8000:lcm=predicate:random_seed=720621696:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 9.73/2.36 % (3596159)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=2179206674:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 9.73/2.36 % (3596162)lrs+10_1_sil=8000:sp=occurrence:random_seed=1432135835:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 9.73/2.36 % (3596163)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4025270777:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 9.73/2.36 % (3596165)Instruction limit reached!
% 9.73/2.36 % (3596165)------------------------------
% 9.73/2.36 % (3596165)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.73/2.36 % (3596165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.73/2.36 % (3596165)CaDiCaL version: 2.1.3
% 9.73/2.36 % (3596165)Termination reason: Instruction limit
% 9.73/2.36 % (3596165)Termination phase: Saturation
% 9.73/2.36 % (3596165)Time elapsed: 0.113 s
% 9.73/2.36 % (3596165)Peak memory usage: 89 MB
% 9.73/2.36 % (3596165)Instructions burned: 117 (million)
% 9.73/2.36 % (3596162)Instruction limit reached!
% 9.73/2.36 % (3596162)------------------------------
% 9.73/2.36 % (3596162)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.73/2.36 % (3596162)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.73/2.36 % (3596162)CaDiCaL version: 2.1.3
% 9.73/2.36 % (3596162)Termination reason: Instruction limit
% 9.73/2.36 % (3596162)Termination phase: Saturation
% 9.73/2.36 % (3596162)Time elapsed: 0.114 s
% 9.73/2.36 % (3596162)Peak memory usage: 89 MB
% 9.73/2.36 % (3596162)Instructions burned: 107 (million)
% 9.73/2.36 % (3596163)Instruction limit reached!
% 9.73/2.36 % (3596163)------------------------------
% 9.73/2.36 % (3596163)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.73/2.36 % (3596163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.73/2.36 % (3596163)CaDiCaL version: 2.1.3
% 9.73/2.36 % (3596163)Termination reason: Instruction limit
% 9.73/2.36 % (3596163)Termination phase: Saturation
% 9.73/2.36 % (3596163)Time elapsed: 0.120 s
% 9.73/2.36 % (3596163)Peak memory usage: 89 MB
% 9.73/2.36 % (3596163)Instructions burned: 114 (million)
% 9.73/2.36 % (3596164)Instruction limit reached!
% 9.73/2.36 % (3596164)------------------------------
% 9.73/2.36 % (3596164)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.73/2.36 % (3596164)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.73/2.36 % (3596164)CaDiCaL version: 2.1.3
% 9.73/2.36 % (3596164)Termination reason: Instruction limit
% 9.73/2.36 % (3596164)Termination phase: Saturation
% 9.73/2.36 % (3596164)Time elapsed: 0.195 s
% 9.73/2.36 % (3596164)Peak memory usage: 90 MB
% 9.73/2.36 % (3596164)Instructions burned: 180 (million)
% 9.73/2.36 % (3596173)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=3375609218:i=143:sd=2:aac=none:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/143Mi)
% 9.73/2.36 % (3596173)Refutation not found, incomplete strategy
% 9.73/2.36 % (3596173)------------------------------
% 9.73/2.36 % (3596173)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.73/2.36 % (3596173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.73/2.36 % (3596173)CaDiCaL version: 2.1.3
% 9.73/2.36 % (3596173)Termination reason: Refutation not found, incomplete strategy
% 9.73/2.36 % (3596173)Time elapsed: 0.019 s
% 9.73/2.36 % (3596173)Peak memory usage: 88 MB
% 9.73/2.36 % (3596173)Instructions burned: 16 (million)
% 9.73/2.36 % (3596175)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1972972002:st=4:i=219:sd=3:ss=axioms_2995 on theBenchmark for (2995ds/219Mi)
% 0.21/2.60 % (3596174)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2477482406:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2995 on theBenchmark for (2995ds/189Mi)
% 0.21/2.60 % (3596175)Refutation not found, incomplete strategy
% 0.21/2.60 % (3596175)------------------------------
% 0.21/2.60 % (3596175)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/2.60 % (3596175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/2.60 % (3596175)CaDiCaL version: 2.1.3
% 0.21/2.60 % (3596175)Termination reason: Refutation not found, incomplete strategy
% 0.21/2.60 % (3596175)Time elapsed: 0.028 s
% 0.21/2.60 % (3596175)Peak memory usage: 88 MB
% 0.21/2.60 % (3596175)Instructions burned: 27 (million)
% 0.21/2.60 % (3596176)lrs+10_64_to=lpo:sil=8000:random_seed=2863580161:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 0.21/2.60 % (3596174)Instruction limit reached!
% 0.21/2.60 % (3596174)------------------------------
% 0.21/2.60 % (3596174)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/2.60 % (3596174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/2.60 % (3596174)CaDiCaL version: 2.1.3
% 0.21/2.60 % (3596174)Termination reason: Instruction limit
% 0.21/2.60 % (3596174)Termination phase: Saturation
% 0.21/2.60 % (3596174)Time elapsed: 0.176 s
% 0.21/2.60 % (3596174)Peak memory usage: 90 MB
% 0.21/2.60 % (3596174)Instructions burned: 190 (million)
% 0.21/2.60 % (3596176)Instruction limit reached!
% 0.21/2.60 % (3596176)------------------------------
% 0.21/2.60 % (3596176)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/2.60 % (3596176)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/2.60 % (3596176)CaDiCaL version: 2.1.3
% 0.21/2.60 % (3596176)Termination reason: Instruction limit
% 0.21/2.60 % (3596176)Termination phase: Saturation
% 0.21/2.60 % (3596176)Time elapsed: 0.137 s
% 0.21/2.60 % (3596176)Peak memory usage: 90 MB
% 0.21/2.60 % (3596176)Instructions burned: 127 (million)
% 0.21/2.60 % (3596173)------------------------------
% 0.21/2.60 % (3596173)------------------------------
% 0.21/2.60 % (3596175)------------------------------
% 0.21/2.60 % (3596175)------------------------------
% 0.21/2.60 % (3596181)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=1082559453:avsq=on:i=194:fgj=on:bd=preordered_2991 on theBenchmark for (2991ds/194Mi)
% 0.21/2.60 % (3596182)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=2696229472:i=157:gtg=all_2990 on theBenchmark for (2990ds/157Mi)
% 0.21/2.60 % (3596160)First to succeed.
% 0.21/2.60 % (3596160)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3596154"
% 0.21/2.60 % (3596183)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=2457363951:i=3394:sd=4:ss=included:sgt=64_2989 on theBenchmark for (2989ds/3394Mi)
% 0.21/2.60 % (3596182)Instruction limit reached!
% 0.21/2.60 % (3596182)------------------------------
% 0.21/2.60 % (3596182)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/2.60 % (3596182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/2.60 % (3596182)CaDiCaL version: 2.1.3
% 0.21/2.60 % (3596182)Termination reason: Instruction limit
% 0.21/2.60 % (3596182)Termination phase: Saturation
% 0.21/2.60 % (3596182)Time elapsed: 0.168 s
% 0.21/2.60 % (3596182)Peak memory usage: 91 MB
% 0.21/2.60 % (3596182)Instructions burned: 157 (million)
% 0.21/2.60 % (3596181)Instruction limit reached!
% 0.21/2.60 % (3596181)------------------------------
% 0.21/2.60 % (3596181)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/2.60 % (3596181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/2.60 % (3596181)CaDiCaL version: 2.1.3
% 0.21/2.60 % (3596181)Termination reason: Instruction limit
% 0.21/2.60 % (3596181)Termination phase: Saturation
% 0.21/2.60 % (3596181)Time elapsed: 0.199 s
% 0.21/2.60 % (3596181)Peak memory usage: 91 MB
% 0.21/2.60 % (3596181)Instructions burned: 194 (million)
% 0.21/2.60 % (3596184)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=1516417751:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2988 on theBenchmark for (2988ds/106Mi)
% 0.21/2.60 % (3596160)Refutation found. Thanks to Tanya!
% 0.21/2.60 % SZS status Unsatisfiable for theBenchmark
% 0.21/2.60 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/2.60 % (3596160)------------------------------
% 0.21/2.60 % (3596160)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/2.60 % (3596160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/2.60 % (3596160)CaDiCaL version: 2.1.3
% 0.21/2.60 % (3596160)Termination reason: Refutation
% 0.21/2.60 % (3596160)Time elapsed: 0.974 s
% 0.21/2.60 % (3596160)Peak memory usage: 138 MB
% 0.21/2.60 % (3596160)Instructions burned: 1751 (million)
% 0.21/2.60 % (3596160)------------------------------
% 0.21/2.60 % (3596160)------------------------------
% 0.21/2.60 % (3596154)Success in time 1.461 s
% 0.21/2.60 % Vampire exiting
%------------------------------------------------------------------------------