%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : CSR133^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 : Wed Sep 30 07:47:17 AM UTC 2026
% Result : Theorem 1.00s 0.43s
% Output : Refutation 1.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CSR133^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 % Computer : n009.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 17:55:45 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 Running first-order model finding
% 0.10/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.00/0.42 % (141293)Will run a generic schedule for satisfiability detection.
% 1.00/0.42 % (141300)% WARNING: option uhcvi not known.
% 1.00/0.42 % (141303)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2306774825:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.00/0.42 % (141299)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2215619457_2999 on theBenchmark for (2999ds/0Mi)
% 1.00/0.42 % (141302)dis+10_1_sil=32000:sp=arity:random_seed=2164997488:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.00/0.42 % (141301)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3788255741:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.00/0.42 % (141303)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.00/0.42 % Exception at run slice level
% 1.00/0.42 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.00/0.42 % (141305)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4001921045:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.00/0.43 % (141304)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2129844846:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.00/0.43 % (141300)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1695826825:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.00/0.43 % (141300)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.00/0.43 % (141300)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.00/0.43 % (141314)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3709325225:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.00/0.43 % Exception at run slice level
% 1.00/0.43 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.00/0.43 % (141304)Instruction limit reached!
% 1.00/0.43 % (141304)------------------------------
% 1.00/0.43 % (141304)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.00/0.43 % (141304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.00/0.43 % (141304)CaDiCaL version: 2.1.3
% 1.00/0.43 % (141304)Termination reason: Instruction limit
% 1.00/0.43 % (141304)Termination phase: Saturation
% 1.00/0.43 % (141304)Time elapsed: 0.037 s
% 1.00/0.43 % (141304)Peak memory usage: 13 MB
% 1.00/0.43 % (141304)Instructions burned: 133 (million)
% 1.00/0.43 % (141316)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1357211092:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.00/0.43 % (141317)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=2754720571:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 1.00/0.43 % (141317)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.00/0.43 % (141302)Instruction limit reached!
% 1.00/0.43 % (141302)------------------------------
% 1.00/0.43 % (141302)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.00/0.43 % (141302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.00/0.43 % (141302)CaDiCaL version: 2.1.3
% 1.00/0.43 % (141302)Termination reason: Instruction limit
% 1.00/0.43 % (141302)Termination phase: Saturation
% 1.00/0.43 % (141302)Time elapsed: 0.051 s
% 1.00/0.43 % (141302)Peak memory usage: 12 MB
% 1.00/0.43 % (141302)Instructions burned: 105 (million)
% 1.00/0.43 % (141317)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.00/0.43 % (141303)Instruction limit reached!
% 1.00/0.43 % (141303)------------------------------
% 1.00/0.43 % (141303)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.00/0.43 % (141303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.00/0.43 % (141303)CaDiCaL version: 2.1.3
% 1.00/0.43 % (141303)Termination reason: Instruction limit
% 1.00/0.43 % (141303)Termination phase: Saturation
% 1.00/0.43 % (141303)Time elapsed: 0.056 s
% 1.00/0.43 % (141303)Peak memory usage: 12 MB
% 1.00/0.43 % (141303)Instructions burned: 117 (million)
% 1.00/0.43 % (141320)ott-21_1_sil=16000:fs=off:random_seed=3020831935:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 1.00/0.43 % (141321)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3099749693:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 1.00/0.43 % (141316)Instruction limit reached!
% 1.00/0.43 % (141316)------------------------------
% 1.00/0.43 % (141316)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.00/0.43 % (141316)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.00/0.43 % (141316)CaDiCaL version: 2.1.3
% 1.00/0.43 % (141316)Termination reason: Instruction limit
% 1.00/0.43 % (141316)Termination phase: Saturation
% 1.00/0.43 % (141316)Time elapsed: 0.068 s
% 1.00/0.43 % (141316)Peak memory usage: 12 MB
% 1.00/0.43 % (141316)Instructions burned: 133 (million)
% 1.00/0.43 % (141324)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1058954917:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.00/0.43 % Exception at run slice level
% 1.00/0.43 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.00/0.43 % (141305)Instruction limit reached!
% 1.00/0.43 % (141305)------------------------------
% 1.00/0.43 % (141305)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.00/0.43 % (141305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.00/0.43 % (141305)CaDiCaL version: 2.1.3
% 1.00/0.43 % (141305)Termination reason: Instruction limit
% 1.00/0.43 % (141305)Termination phase: Saturation
% 1.00/0.43 % (141305)Time elapsed: 0.146 s
% 1.00/0.43 % (141305)Peak memory usage: 13 MB
% 1.00/0.43 % (141305)Instructions burned: 160 (million)
% 1.00/0.43 % (141320)Instruction limit reached!
% 1.00/0.43 % (141320)------------------------------
% 1.00/0.43 % (141320)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.00/0.43 % (141320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.00/0.43 % (141320)CaDiCaL version: 2.1.3
% 1.00/0.43 % (141320)Termination reason: Instruction limit
% 1.00/0.43 % (141320)Termination phase: Saturation
% 1.00/0.43 % (141320)Time elapsed: 0.081 s
% 1.00/0.43 % (141320)Peak memory usage: 12 MB
% 1.00/0.43 % (141320)Instructions burned: 182 (million)
% 1.00/0.43 % (141317) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-141293-141317"...
% 1.00/0.43 % (141326)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3612442202:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 1.00/0.43 % (141317)...printing done.
% 1.00/0.43 % (141317)Refutation found. Thanks to Tanya!
% 1.00/0.43 % SZS status Theorem for theBenchmark
% 1.00/0.43 % SZS output start Proof for theBenchmark
% 1.00/0.43 thf(type_def_5, type, num: $tType).
% 1.00/0.43 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 1.00/0.43 thf(func_def_0, type, holdsDuring_THFTYPE_IiooI: ($i > $o > $o)).
% 1.00/0.43 thf(func_def_7, type, lYearFn_THFTYPE_IiiI: ($i > $i)).
% 1.00/0.43 thf(func_def_8, type, likes_THFTYPE_IiioI: ($i > $i > $o)).
% 1.00/0.43 thf(func_def_10, type, parent_THFTYPE_IiioI: ($i > $i > $o)).
% 1.00/0.43 thf(func_def_12, type, vNOT: ($o > $o)).
% 1.00/0.43 thf(func_def_15, type, vAND: ($o > $o > $o)).
% 1.00/0.43 thf(func_def_16, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.00/0.43 thf(func_def_17, type, db0: !>[X0: $tType]:(X0)).
% 1.00/0.43 thf(func_def_18, type, db1: !>[X0: $tType]:(X0)).
% 1.00/0.43 thf(func_def_19, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.00/0.43 thf(func_def_20, type, db2: !>[X0: $tType]:(X0)).
% 1.00/0.43 thf(f2,axiom,(
% 1.00/0.43 (holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBen_THFTYPE_i))),
% 1.00/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_001)).
% 1.00/0.43 thf(f3,axiom,(
% 1.00/0.43 (holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (~ (parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lAnna_THFTYPE_i)))),
% 1.00/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_002)).
% 1.00/0.43 thf(f11,conjecture,(
% 1.00/0.43 ? [X0 : ($i > $i > $o),X1 : ($i > $i > $o),X2 : $i] : (holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (~ (X1 = X0)) & (X0 @ X2 @ lAnna_THFTYPE_i) & (X1 @ X2 @ lBill_THFTYPE_i))),
% 1.00/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',con)).
% 1.00/0.43 thf(f12,negated_conjecture,(
% 1.00/0.43 ~ ? [X0 : ($i > $i > $o),X1 : ($i > $i > $o),X2 : $i] : (holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (~ (X1 = X0)) & (X0 @ X2 @ lAnna_THFTYPE_i) & (X1 @ X2 @ lBill_THFTYPE_i))),
% 1.00/0.43 inference(negated_conjecture,[status(cth)],[f11])).
% 1.00/0.43 thf(f15,plain,(
% 1.00/0.43 (holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBen_THFTYPE_i))),
% 1.00/0.43 inference(rectify,[],[f2])).
% 1.00/0.43 thf(f16,plain,(
% 1.00/0.43 (((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBen_THFTYPE_i))) = $true)),
% 1.00/0.43 inference(fool_elimination,[],[f15])).
% 1.00/0.43 thf(f17,plain,(
% 1.00/0.43 (holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (~ (parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lAnna_THFTYPE_i)))),
% 1.00/0.43 inference(rectify,[],[f3])).
% 1.00/0.43 thf(f18,plain,(
% 1.00/0.43 (((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (~ (parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lAnna_THFTYPE_i)))) = $true)),
% 1.00/0.43 inference(fool_elimination,[],[f17])).
% 1.00/0.43 thf(f33,plain,(
% 1.00/0.43 ~ ? [X0 : ($i > $i > $o),X1 : ($i > $i > $o),X2 : $i] : (holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (~ (X1 = X0)) & (X0 @ X2 @ lAnna_THFTYPE_i) & (X1 @ X2 @ lBill_THFTYPE_i))),
% 1.00/0.43 inference(rectify,[],[f12])).
% 1.00/0.43 thf(f34,plain,(
% 1.00/0.43 ~ ? [X0 : ($i > $i > $o),X1 : ($i > $i > $o),X2 : $i] : ($true = ((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (((X1 @ X2 @ lBill_THFTYPE_i) & (X0 @ X2 @ lAnna_THFTYPE_i)) & (~ (X0 = X1))))))),
% 1.00/0.43 inference(fool_elimination,[],[f33])).
% 1.00/0.43 thf(f35,plain,(
% 1.00/0.43 ! [X0 : ($i > $i > $o),X1 : ($i > $i > $o),X2 : $i] : ($true != ((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (((X1 @ X2 @ lBill_THFTYPE_i) & (X0 @ X2 @ lAnna_THFTYPE_i)) & (~ (X0 = X1))))))),
% 1.00/0.43 inference(ennf_transformation,[],[f34])).
% 1.00/0.43 thf(f37,plain,(
% 1.00/0.43 (((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBen_THFTYPE_i))) = $true)),
% 1.00/0.43 inference(cnf_transformation,[],[f16])).
% 1.00/0.43 thf(f38,plain,(
% 1.00/0.43 (((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (~ (parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lAnna_THFTYPE_i)))) = $true)),
% 1.00/0.43 inference(cnf_transformation,[],[f18])).
% 1.00/0.43 thf(f46,plain,(
% 1.00/0.43 ( ! [X2 : $i,X0 : ($i > $i > $o),X1 : ($i > $i > $o)] : (($true != ((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (((X1 @ X2 @ lBill_THFTYPE_i) & (X0 @ X2 @ lAnna_THFTYPE_i)) & (~ (X0 = X1))))))) )),
% 1.00/0.43 inference(cnf_transformation,[],[f35])).
% 1.00/0.43 thf(f47,definition,(
% 1.00/0.43 ($true != $false)),
% 1.00/0.43 introduced(theory,[fool_distinctness_axiom])).
% 1.00/0.43 thf(f48,definition,(
% 1.00/0.43 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 1.00/0.43 introduced(theory,[fool_exhaustiveness_axiom])).
% 1.00/0.43 thf(f59,plain,(
% 1.00/0.43 ( ! [X2 : ($i > $i > $o),X0 : ($i > $i > $o),X1 : $i] : (($true != ((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (((X0 @ X1 @ lBill_THFTYPE_i) & (X2 @ X1 @ lAnna_THFTYPE_i)) & (~ $true))))) | ($false = ((X2 = X0)))) )),
% 1.00/0.43 inference(constrained_superposition,[],[f46,f48])).
% 1.00/0.43 thf(f80,plain,(
% 1.00/0.43 ( ! [X2 : ($i > $i > $o),X0 : ($i > $i > $o),X1 : $i] : (($true != ((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (((X0 @ X1 @ lBill_THFTYPE_i) & (X2 @ X1 @ lAnna_THFTYPE_i)) & (~ $true))))) | (X0 != X2)) )),
% 1.00/0.43 inference(equality_proxy_clausification,[],[f59])).
% 1.00/0.43 thf(f81,plain,(
% 1.00/0.43 ( ! [X2 : ($i > $i > $o),X0 : ($i > $i > $o),X1 : $i] : (($true != ((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (((X0 @ X1 @ lBill_THFTYPE_i) & (X2 @ X1 @ lAnna_THFTYPE_i)) & $false)))) | (X0 != X2)) )),
% 1.00/0.43 inference(boolean_simplification,[],[f80])).
% 1.00/0.43 thf(f82,plain,(
% 1.00/0.43 ( ! [X2 : ($i > $i > $o),X0 : ($i > $i > $o)] : (($true != ((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ $false))) | (X0 != X2)) )),
% 1.00/0.43 inference(boolean_simplification,[],[f81])).
% 1.00/0.43 thf(f92,definition,(
% 1.00/0.43 spl0_2 <=> ($true = ((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ $true)))),
% 1.00/0.43 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 1.00/0.43 thf(f97,definition,(
% 1.00/0.43 spl0_3 <=> ! [X2 : ($i > $i > $o),X0 : ($i > $i > $o),X1 : $i] : ((X0 = X2) | ($false = ((X0 @ X1 @ lBill_THFTYPE_i))) | ($false = ((X2 @ X1 @ lAnna_THFTYPE_i))))),
% 1.00/0.43 introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition])).
% 1.00/0.43 thf(f98,plain,(
% 1.00/0.43 ( ! [X2 : ($i > $i > $o),X0 : ($i > $i > $o),X1 : $i] : ((X0 = X2) | ($false = ((X0 @ X1 @ lBill_THFTYPE_i))) | ($false = ((X2 @ X1 @ lAnna_THFTYPE_i)))) ) | ~spl0_3),
% 1.00/0.43 inference(avatar_component_clause,[],[f97])).
% 1.00/0.43 thf(f101,definition,(
% 1.00/0.43 spl0_4 <=> ! [X2 : ($i > $i > $o),X0 : ($i > $i > $o)] : (X0 != X2)),
% 1.00/0.43 introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition])).
% 1.00/0.43 thf(f102,plain,(
% 1.00/0.43 ( ! [X2 : ($i > $i > $o),X0 : ($i > $i > $o)] : ((X0 != X2)) ) | ~spl0_4),
% 1.00/0.43 inference(avatar_component_clause,[],[f101])).
% 1.00/0.43 thf(f104,definition,(
% 1.00/0.43 spl0_5 <=> ($true = ((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ $false)))),
% 1.00/0.43 introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition])).
% 1.00/0.43 thf(f106,plain,(
% 1.00/0.43 ($true != ((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ $false))) | spl0_5),
% 1.00/0.43 inference(avatar_component_clause,[],[f104])).
% 1.00/0.43 thf(f107,plain,(
% 1.00/0.43 spl0_4 | ~spl0_5),
% 1.00/0.43 inference(avatar_split_clause,[],[f82,f104,f101])).
% 1.00/0.43 thf(f108,plain,(
% 1.00/0.43 $false | ~spl0_4),
% 1.00/0.43 inference(flex-flex_simplification,[],[f102])).
% 1.00/0.43 thf(f109,plain,(
% 1.00/0.43 ~spl0_4),
% 1.00/0.43 inference(avatar_contradiction_clause,[],[f108])).
% 1.00/0.43 thf(f110,plain,(
% 1.00/0.43 ($true != $true) | ($false = ((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ $false))) | spl0_5),
% 1.00/0.43 inference(constrained_superposition,[],[f106,f48])).
% 1.00/0.43 thf(f111,plain,(
% 1.00/0.43 ($false = ((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ $false))) | spl0_5),
% 1.00/0.43 inference(trivial_inequality_removal,[],[f110])).
% 1.00/0.43 thf(f128,plain,(
% 1.00/0.43 ( ! [X0 : ($i > $i > $o),X1 : $i] : (((^[Y0 : $i]: ((^[Y1 : $i]: (Y0 = Y1)))) = X0) | ($false = ((X0 @ X1 @ lBill_THFTYPE_i))) | ($false = (((^[Y0 : $i]: ((^[Y1 : $i]: (Y0 = Y1)))) @ X1 @ lAnna_THFTYPE_i)))) ) | ~spl0_3),
% 1.00/0.43 inference(primitive_instantiation,[],[f98])).
% 1.00/0.43 thf(f362,plain,(
% 1.00/0.43 ( ! [X0 : ($i > $i > $o),X1 : $i] : ((= = X0) | ($false = ((X0 @ X1 @ lBill_THFTYPE_i))) | ($false = ((X1 = lAnna_THFTYPE_i)))) ) | ~spl0_3),
% 1.00/0.43 inference(beta-eta_normalization,[],[f128])).
% 1.00/0.43 thf(f363,plain,(
% 1.00/0.43 ( ! [X0 : ($i > $i > $o),X1 : $i] : ((lAnna_THFTYPE_i != X1) | ($false = ((X0 @ X1 @ lBill_THFTYPE_i))) | (= = X0)) ) | ~spl0_3),
% 1.00/0.43 inference(equality_proxy_clausification,[],[f362])).
% 1.00/0.43 thf(f481,plain,(
% 1.00/0.43 ( ! [X0 : ($i > $i > $o)] : (($false = ((X0 @ lAnna_THFTYPE_i @ lBill_THFTYPE_i))) | (= = X0)) ) | ~spl0_3),
% 1.00/0.43 inference(equality_resolution,[],[f363])).
% 1.00/0.43 thf(f489,plain,(
% 1.00/0.43 ($false != $false) | ((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) = =) | ~spl0_3),
% 1.00/0.43 inference(constrained_superposition,[],[f47,f481])).
% 1.00/0.43 thf(f588,plain,(
% 1.00/0.43 ((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) = =) | ~spl0_3),
% 1.00/0.43 inference(trivial_inequality_removal,[],[f489])).
% 1.00/0.43 thf(f626,plain,(
% 1.00/0.43 ( ! [X2 : ($i > $i > $o),X0 : ($i > $i > $o),X1 : $i] : (($true != ((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ $true))) | ($false = ((((X0 @ X1 @ lBill_THFTYPE_i) & (X2 @ X1 @ lAnna_THFTYPE_i)) & (~ (X2 = X0)))))) )),
% 1.00/0.43 inference(constrained_superposition,[],[f46,f48])).
% 1.00/0.43 thf(f640,plain,(
% 1.00/0.43 ( ! [X2 : ($i > $i > $o),X0 : ($i > $i > $o),X1 : $i] : (($true != ((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ $true))) | ($false = ((~ (X2 = X0)))) | ($false = (((X0 @ X1 @ lBill_THFTYPE_i) & (X2 @ X1 @ lAnna_THFTYPE_i))))) )),
% 1.00/0.43 inference(and_proxy_clausification,[],[f626])).
% 1.00/0.43 thf(f641,plain,(
% 1.00/0.43 ( ! [X2 : ($i > $i > $o),X0 : ($i > $i > $o),X1 : $i] : (($true != ((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ $true))) | ($true = ((X2 = X0))) | ($false = (((X0 @ X1 @ lBill_THFTYPE_i) & (X2 @ X1 @ lAnna_THFTYPE_i))))) )),
% 1.00/0.43 inference(not_proxy_clausification,[],[f640])).
% 1.00/0.43 thf(f642,plain,(
% 1.00/0.43 ( ! [X2 : ($i > $i > $o),X0 : ($i > $i > $o),X1 : $i] : (($true != ((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ $true))) | (X0 = X2) | ($false = (((X0 @ X1 @ lBill_THFTYPE_i) & (X2 @ X1 @ lAnna_THFTYPE_i))))) )),
% 1.00/0.43 inference(equality_proxy_clausification,[],[f641])).
% 1.00/0.43 thf(f643,plain,(
% 1.00/0.43 ( ! [X2 : ($i > $i > $o),X0 : ($i > $i > $o),X1 : $i] : (($true != ((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ $true))) | (X0 = X2) | ($false = ((X2 @ X1 @ lAnna_THFTYPE_i))) | ($false = ((X0 @ X1 @ lBill_THFTYPE_i)))) )),
% 1.00/0.43 inference(and_proxy_clausification,[],[f642])).
% 1.00/0.43 thf(f661,plain,(
% 1.00/0.43 spl0_3 | ~spl0_2),
% 1.00/0.43 inference(avatar_split_clause,[],[f643,f92,f97])).
% 1.00/0.43 thf(f668,plain,(
% 1.00/0.43 ( ! [X1 : $i] : (((((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) @ X1)) = ((= @ X1)))) ) | ~spl0_3),
% 1.00/0.43 inference(argument_congruence,[],[f588])).
% 1.00/0.43 thf(f669,plain,(
% 1.00/0.43 ( ! [X1 : $i] : (((^[Y0 : $i]: ($true)) = ((= @ X1)))) ) | ~spl0_3),
% 1.00/0.43 inference(beta-eta_normalization,[],[f668])).
% 1.00/0.43 thf(f670,plain,(
% 1.00/0.43 ( ! [X2 : $i,X1 : $i] : (((((^[Y0 : $i]: ($true)) @ X2)) = ((X1 = X2)))) ) | ~spl0_3),
% 1.00/0.43 inference(argument_congruence,[],[f669])).
% 1.00/0.43 thf(f672,plain,(
% 1.00/0.43 ( ! [X2 : $i,X1 : $i] : (($false = (((^[Y0 : $i]: ($true)) @ X2))) | ($true = ((X1 = X2)))) ) | ~spl0_3),
% 1.00/0.43 inference(iff_proxy_clausification,[],[f670])).
% 1.00/0.43 thf(f673,plain,(
% 1.00/0.43 ( ! [X2 : $i,X1 : $i] : (($false = (((^[Y0 : $i]: ($true)) @ X2))) | (X1 = X2)) ) | ~spl0_3),
% 1.00/0.43 inference(equality_proxy_clausification,[],[f672])).
% 1.00/0.43 thf(f674,plain,(
% 1.00/0.43 ( ! [X2 : $i,X1 : $i] : (($true = $false) | (X1 = X2)) ) | ~spl0_3),
% 1.00/0.43 inference(beta-eta_normalization,[],[f673])).
% 1.00/0.43 thf(f675,plain,(
% 1.00/0.43 ( ! [X2 : $i,X1 : $i] : ((X1 = X2)) ) | ~spl0_3),
% 1.00/0.43 inference(trivial_inequality_removal,[],[f674])).
% 1.00/0.43 thf(f692,plain,(
% 1.00/0.43 ( ! [X0 : $i] : (($false = ((holdsDuring_THFTYPE_IiooI @ X0 @ $false)))) ) | (~spl0_3 | spl0_5)),
% 1.00/0.43 inference(constrained_superposition,[],[f111,f675])).
% 1.00/0.43 thf(f739,plain,(
% 1.00/0.43 ( ! [X0 : $i] : (($true = ((holdsDuring_THFTYPE_IiooI @ X0 @ (parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBen_THFTYPE_i))))) ) | ~spl0_3),
% 1.00/0.43 inference(constrained_superposition,[],[f37,f675])).
% 1.00/0.43 thf(f759,definition,(
% 1.00/0.43 spl0_13 <=> (((parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBen_THFTYPE_i)) = $false)),
% 1.00/0.43 introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition])).
% 1.00/0.43 thf(f760,plain,(
% 1.00/0.43 (((parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBen_THFTYPE_i)) != $false) | spl0_13),
% 1.00/0.43 inference(avatar_component_clause,[],[f759])).
% 1.00/0.43 thf(f761,plain,(
% 1.00/0.43 (((parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBen_THFTYPE_i)) = $false) | ~spl0_13),
% 1.00/0.43 inference(avatar_component_clause,[],[f759])).
% 1.00/0.43 thf(f1894,plain,(
% 1.00/0.43 ( ! [X0 : $i] : (($true = ((holdsDuring_THFTYPE_IiooI @ X0 @ $false)))) ) | (~spl0_3 | ~spl0_13)),
% 1.00/0.43 inference(constrained_superposition,[],[f739,f761])).
% 1.00/0.43 thf(f1908,plain,(
% 1.00/0.43 ($true = $false) | (~spl0_3 | spl0_5 | ~spl0_13)),
% 1.00/0.43 inference(forward_demodulation,[],[f1894,f692])).
% 1.00/0.43 thf(f1909,plain,(
% 1.00/0.43 $false | (~spl0_3 | spl0_5 | ~spl0_13)),
% 1.00/0.43 inference(trivial_inequality_removal,[],[f1908])).
% 1.00/0.43 thf(f1910,plain,(
% 1.00/0.43 ~spl0_3 | spl0_5 | ~spl0_13),
% 1.00/0.43 inference(avatar_contradiction_clause,[],[f1909])).
% 1.00/0.43 thf(f1911,plain,(
% 1.00/0.43 ( ! [X0 : $i] : (($false != ((parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ X0)))) ) | (~spl0_3 | spl0_13)),
% 1.00/0.43 inference(constrained_superposition,[],[f760,f675])).
% 1.00/0.43 thf(f2000,plain,(
% 1.00/0.43 ( ! [X0 : $i,X1 : $i] : (($false != ((parent_THFTYPE_IiioI @ X0 @ X1)))) ) | (~spl0_3 | spl0_13)),
% 1.00/0.43 inference(constrained_superposition,[],[f1911,f675])).
% 1.00/0.43 thf(f4943,plain,(
% 1.00/0.43 ($true = ((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (~ $true)))) | (((parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lAnna_THFTYPE_i)) = $false)),
% 1.00/0.43 inference(constrained_superposition,[],[f38,f48])).
% 1.00/0.43 thf(f4956,plain,(
% 1.00/0.43 ($true = ((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ $true))) | (((~ (parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lAnna_THFTYPE_i))) = $false)),
% 1.00/0.43 inference(constrained_superposition,[],[f38,f48])).
% 1.00/0.43 thf(f5143,plain,(
% 1.00/0.43 ($true = ((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ $true))) | (((parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lAnna_THFTYPE_i)) = $true)),
% 1.00/0.43 inference(not_proxy_clausification,[],[f4956])).
% 1.00/0.43 thf(f5156,plain,(
% 1.00/0.43 ($true = ((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ $false))) | (((parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lAnna_THFTYPE_i)) = $false)),
% 1.00/0.43 inference(boolean_simplification,[],[f4943])).
% 1.00/0.43 thf(f5285,plain,(
% 1.00/0.43 (((parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lAnna_THFTYPE_i)) = $false) | spl0_5),
% 1.00/0.43 inference(forward_subsumption_resolution,[],[f5156,f106])).
% 1.00/0.43 thf(f5288,definition,(
% 1.00/0.43 spl0_29 <=> (((parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lAnna_THFTYPE_i)) = $true)),
% 1.00/0.43 introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition])).
% 1.00/0.43 thf(f5290,plain,(
% 1.00/0.43 (((parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lAnna_THFTYPE_i)) = $true) | ~spl0_29),
% 1.00/0.43 inference(avatar_component_clause,[],[f5288])).
% 1.00/0.43 thf(f5393,plain,(
% 1.00/0.43 $false | (~spl0_3 | spl0_5 | spl0_13)),
% 1.00/0.43 inference(forward_subsumption_resolution,[],[f5285,f2000])).
% 1.00/0.43 thf(f5394,plain,(
% 1.00/0.43 ~spl0_3 | spl0_5 | spl0_13),
% 1.00/0.43 inference(avatar_contradiction_clause,[],[f5393])).
% 1.00/0.43 thf(f5412,plain,(
% 1.00/0.43 spl0_29 | spl0_2),
% 1.00/0.43 inference(avatar_split_clause,[],[f5143,f92,f5288])).
% 1.00/0.43 thf(f5501,plain,(
% 1.00/0.43 ($true = $false) | (spl0_5 | ~spl0_29)),
% 1.00/0.43 inference(forward_demodulation,[],[f5290,f5285])).
% 1.00/0.43 thf(f5502,plain,(
% 1.00/0.43 $false | (spl0_5 | ~spl0_29)),
% 1.00/0.43 inference(trivial_inequality_removal,[],[f5501])).
% 1.00/0.43 thf(f5503,plain,(
% 1.00/0.43 spl0_5 | ~spl0_29),
% 1.00/0.43 inference(avatar_contradiction_clause,[],[f5502])).
% 1.00/0.43 cnf(s3, plain, spl0_4 | ~spl0_5, inference(sat_conversion,[],[f107])).
% 1.00/0.43 cnf(s4, plain, ~spl0_4, inference(sat_conversion,[],[f109])).
% 1.00/0.43 cnf(s18, plain, ~spl0_2 | spl0_3, inference(sat_conversion,[],[f661])).
% 1.00/0.43 cnf(s27, plain, ~spl0_3 | spl0_5 | ~spl0_13, inference(sat_conversion,[],[f1910])).
% 1.00/0.43 cnf(s82, plain, ~spl0_3 | spl0_5 | spl0_13, inference(sat_conversion,[],[f5394])).
% 1.00/0.43 cnf(s84, plain, spl0_2 | spl0_29, inference(sat_conversion,[],[f5412])).
% 1.00/0.43 cnf(s90, plain, spl0_5 | ~spl0_29, inference(sat_conversion,[],[f5503])).
% 1.00/0.43 cnf(s95, plain, ~spl0_5, inference(rat,[],[s3,s4])).
% 1.00/0.43 cnf(s96, plain, ~spl0_29, inference(rat,[],[s90,s95])).
% 1.00/0.43 cnf(s99, plain, spl0_2, inference(rat,[],[s84,s96])).
% 1.00/0.43 cnf(s100, plain, spl0_3, inference(rat,[],[s18,s99])).
% 1.00/0.43 cnf(s101, plain, spl0_13, inference(rat,[],[s82,s95,s100])).
% 1.00/0.43 cnf(s117, plain, $false, inference(rat,[],[s27,s95,s101,s100])).
% 1.00/0.43 thf(f5504,plain,(
% 1.00/0.43 $false),
% 1.00/0.43 inference(avatar_sat_refutation,[],[s117])).
% 1.00/0.43 % SZS output end Proof for theBenchmark
% 1.00/0.43 % (141317)------------------------------
% 1.00/0.43 % (141317)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.00/0.43 % (141317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.00/0.43 % (141317)CaDiCaL version: 2.1.3
% 1.00/0.43 % (141317)Termination reason: Refutation
% 1.00/0.43 % (141317)Time elapsed: 0.106 s
% 1.00/0.43 % (141317)Peak memory usage: 14 MB
% 1.00/0.43 % (141317)Instructions burned: 378 (million)
% 1.00/0.43 % (141293)Success in time 0.191 s
% 1.00/0.43 % Vampire exiting
%------------------------------------------------------------------------------