%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL776-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 12:00:33 PM UTC 2026
% Result : Unsatisfiable 1.63s 0.72s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 16 ( 10 unt; 0 def)
% Number of atoms : 24 ( 3 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 11 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-5 aty)
% Number of variables : 30 ( 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f937,axiom,
! [X2,X0,X1] : hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2) = c_List_Ofoldl(c_Lambda_OdB_OApp,X0,c_List_Oappend(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_app__last_0) ).
fof(f980,axiom,
! [X2,X0,X1] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0)),X1),X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X0,X1,c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Beta_0) ).
fof(f994,axiom,
! [X2,X3,X0,X1,X4,X5] : c_List_Ofoldl(X0,X1,c_List_Olist_OCons(X2,X3,X4),X5,X4) = c_List_Ofoldl(X0,hAPP(hAPP(X0,X1),X2),X3,X5,X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__Cons_0) ).
fof(f997,axiom,
! [X2,X3,X0,X1] : c_List_Oappend(c_List_Olist_OCons(X0,X1,X2),X3,X2) = c_List_Olist_OCons(X0,c_List_Oappend(X1,X3,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).
fof(f1022,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1023,negated_conjecture,
hBOOL(hAPP(c_InductTermi_OIT,v_s)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f1025,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r)),v_s),c_List_Oappend(v_ss,c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f4044,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r)),v_s),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
inference(superposition,[],[f1025,f937]) ).
fof(f4072,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r),c_List_Olist_OCons(v_s,v_ss,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
inference(forward_demodulation,[],[f4044,f994]) ).
fof(f4576,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X1))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0),c_List_Olist_OCons(X1,X2,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X0,X1,c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(forward_demodulation,[],[f980,f994]) ).
fof(f4624,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X0,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_Lambda_OdB,tc_Lambda_OdB)))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0),c_List_Olist_OCons(v_s,X1,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(resolution,[],[f4576,f1023]) ).
fof(f4644,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X0,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2)))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0),c_List_Olist_OCons(v_s,c_List_Oappend(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))) ),
inference(superposition,[],[f4624,f937]) ).
fof(f4648,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0),c_List_Oappend(c_List_Olist_OCons(v_s,X1,tc_Lambda_OdB),c_List_Olist_OCons(X2,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X0,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2))) ),
inference(forward_demodulation,[],[f4644,f997]) ).
fof(f4660,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(X0,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2)))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0),c_List_Olist_OCons(v_s,X1,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)),X2))) ),
inference(forward_demodulation,[],[f4648,f937]) ).
fof(f4886,plain,
hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r),c_List_Olist_OCons(v_s,v_ss,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))),
inference(resolution,[],[f4660,f1022]) ).
fof(f4922,plain,
$false,
inference(forward_subsumption_resolution,[],[f4886,f4072]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL776-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n016.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 16:52:32 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.63/0.72 % (2840894)Will run a generic schedule for satisfiability detection.
% 1.63/0.72 % (2840905)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2872312472:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.63/0.72 % (2840900)% WARNING: option uhcvi not known.
% 1.63/0.72 % (2840900)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=595172112:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.63/0.72 % (2840899)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3745126521_2999 on theBenchmark for (2999ds/0Mi)
% 1.63/0.72 % (2840901)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2379353801:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.63/0.72 % (2840902)dis+10_1_sil=32000:sp=arity:random_seed=356732543:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.63/0.72 % (2840904)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3171168197:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.63/0.72 % (2840903)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3277202473:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.63/0.72 % (2840905)Instruction limit reached!
% 1.63/0.72 % (2840905)------------------------------
% 1.63/0.72 % (2840905)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.63/0.72 % (2840905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.63/0.72 % (2840905)CaDiCaL version: 2.1.3
% 1.63/0.72 % (2840905)Termination reason: Instruction limit
% 1.63/0.72 % (2840905)Termination phase: Saturation
% 1.63/0.72 % (2840905)Time elapsed: 0.058 s
% 1.63/0.72 % (2840905)Peak memory usage: 14 MB
% 1.63/0.72 % (2840905)Instructions burned: 161 (million)
% 1.63/0.72 % (2840902)Instruction limit reached!
% 1.63/0.72 % (2840902)------------------------------
% 1.63/0.72 % (2840902)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.63/0.72 % (2840902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.63/0.72 % (2840902)CaDiCaL version: 2.1.3
% 1.63/0.72 % (2840902)Termination reason: Instruction limit
% 1.63/0.72 % (2840902)Termination phase: Saturation
% 1.63/0.72 % (2840902)Time elapsed: 0.066 s
% 1.63/0.72 % (2840902)Peak memory usage: 13 MB
% 1.63/0.72 % (2840902)Instructions burned: 103 (million)
% 1.63/0.72 % (2840903)Instruction limit reached!
% 1.63/0.72 % (2840903)------------------------------
% 1.63/0.72 % (2840903)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.63/0.72 % (2840903)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.63/0.72 % (2840903)CaDiCaL version: 2.1.3
% 1.63/0.72 % (2840903)Termination reason: Instruction limit
% 1.63/0.72 % (2840903)Termination phase: Saturation
% 1.63/0.72 % (2840903)Time elapsed: 0.074 s
% 1.63/0.72 % (2840903)Peak memory usage: 13 MB
% 1.63/0.72 % (2840903)Instructions burned: 117 (million)
% 1.63/0.72 % (2840904)Instruction limit reached!
% 1.63/0.72 % (2840904)------------------------------
% 1.63/0.72 % (2840904)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.63/0.72 % (2840904)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.63/0.72 % (2840904)CaDiCaL version: 2.1.3
% 1.63/0.72 % (2840904)Termination reason: Instruction limit
% 1.63/0.72 % (2840904)Termination phase: Saturation
% 1.63/0.72 % (2840904)Time elapsed: 0.079 s
% 1.63/0.72 % (2840904)Peak memory usage: 13 MB
% 1.63/0.72 % (2840904)Instructions burned: 131 (million)
% 1.63/0.72 % (2840913)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1850512419:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.63/0.72 % (2840914)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=574864330:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.63/0.72 % (2840916)ott-21_1_sil=16000:fs=off:random_seed=2661189702:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.63/0.72 % (2840915)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3274204203:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.63/0.72 % TRYING [1]
% 1.63/0.72 % TRYING [1]
% 1.63/0.72 % TRYING [2]
% 1.63/0.72 % TRYING [2]
% 1.63/0.72 % (2840914)Instruction limit reached!
% 1.63/0.72 % (2840914)------------------------------
% 1.63/0.72 % (2840914)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.63/0.72 % (2840914)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.63/0.72 % (2840914)CaDiCaL version: 2.1.3
% 1.63/0.72 % (2840914)Termination reason: Instruction limit
% 1.63/0.72 % (2840914)Termination phase: Saturation
% 1.63/0.72 % (2840914)Time elapsed: 0.083 s
% 1.63/0.72 % (2840914)Peak memory usage: 13 MB
% 1.63/0.72 % (2840914)Instructions burned: 132 (million)
% 1.63/0.72 % (2840916)Instruction limit reached!
% 1.63/0.72 % (2840916)------------------------------
% 1.63/0.72 % (2840916)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.63/0.72 % (2840916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.63/0.72 % (2840916)CaDiCaL version: 2.1.3
% 1.63/0.72 % (2840916)Termination reason: Instruction limit
% 1.63/0.72 % (2840916)Termination phase: Saturation
% 1.63/0.72 % (2840916)Time elapsed: 0.086 s
% 1.63/0.72 % (2840916)Peak memory usage: 12 MB
% 1.63/0.72 % (2840916)Instructions burned: 180 (million)
% 1.63/0.72 % (2840921)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2164187320:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 1.63/0.72 % (2840922)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3236459653:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 1.63/0.72 % TRYING [3]
% 1.63/0.72 % (2840915) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2840894-2840915"...
% 1.63/0.72 % (2840913)Instruction limit reached!
% 1.63/0.72 % (2840913)------------------------------
% 1.63/0.72 % (2840913)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.63/0.72 % (2840913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.63/0.72 % (2840913)CaDiCaL version: 2.1.3
% 1.63/0.72 % (2840913)Termination reason: Instruction limit
% 1.63/0.72 % (2840913)Termination phase: Finite model building constraint generation
% 1.63/0.72 % (2840913)Time elapsed: 0.163 s
% 1.63/0.72 % (2840913)Peak memory usage: 32 MB
% 1.63/0.72 % (2840913)Instructions burned: 718 (million)
% 1.63/0.72 % (2840915)...printing done.
% 1.63/0.72 % (2840915)Refutation found. Thanks to Tanya!
% 1.63/0.72 % SZS status Unsatisfiable for theBenchmark
% 1.63/0.72 % SZS output start Proof for theBenchmark
% See solution above
% 1.63/0.72 % (2840915)------------------------------
% 1.63/0.72 % (2840915)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.63/0.72 % (2840915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.63/0.72 % (2840915)CaDiCaL version: 2.1.3
% 1.63/0.72 % (2840915)Termination reason: Refutation
% 1.63/0.72 % (2840915)Time elapsed: 0.145 s
% 1.63/0.72 % (2840915)Peak memory usage: 15 MB
% 1.63/0.72 % (2840915)Instructions burned: 240 (million)
% 1.63/0.72 % (2840894)Success in time 0.3 s
% 1.63/0.72 % Vampire exiting
%------------------------------------------------------------------------------