%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP083^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 08:08:16 AM UTC 2026
% Result : Theorem 0.27s 0.40s
% Output : Refutation 0.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP083^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n026.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 19:52:59 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.21/0.29 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.27/0.40 % (1097059)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.27/0.40 % (1097067)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3360750139:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.27/0.40 % (1097064)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1742485361:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.27/0.40 % (1097065)lrs+10_16_si=on:nwc=1.5:random_seed=3712303926:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.27/0.40 % (1097066)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=270136848:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.27/0.40 % (1097068)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=336158791:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.27/0.40 % (1097066)Instruction limit reached!
% 0.27/0.40 % (1097066)------------------------------
% 0.27/0.40 % (1097066)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.27/0.40 % (1097066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/0.40 % (1097066)CaDiCaL version: 2.1.3
% 0.27/0.40 % (1097066)Termination reason: Instruction limit
% 0.27/0.40 % (1097066)Termination phase: shuffling
% 0.27/0.40 % (1097066)Time elapsed: 0.002 s
% 0.27/0.40 % (1097066)Peak memory usage: 10 MB
% 0.27/0.40 % (1097066)Instructions burned: 4 (million)
% 0.27/0.40 % (1097065)Instruction limit reached!
% 0.27/0.40 % (1097065)------------------------------
% 0.27/0.40 % (1097065)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.27/0.40 % (1097065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/0.40 % (1097065)CaDiCaL version: 2.1.3
% 0.27/0.40 % (1097065)Termination reason: Instruction limit
% 0.27/0.40 % (1097065)Termination phase: shuffling
% 0.27/0.40 % (1097065)Time elapsed: 0.009 s
% 0.27/0.40 % (1097065)Peak memory usage: 10 MB
% 0.27/0.40 % (1097065)Instructions burned: 19 (million)
% 0.27/0.40 % (1097070)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.27/0.40 % (1097070)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.27/0.40 % (1097068)Instruction limit reached!
% 0.27/0.40 % (1097068)------------------------------
% 0.27/0.40 % (1097068)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.27/0.40 % (1097068)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/0.40 % (1097068)CaDiCaL version: 2.1.3
% 0.27/0.40 % (1097068)Termination reason: Instruction limit
% 0.27/0.40 % (1097068)Termination phase: shuffling
% 0.27/0.40 % (1097068)Time elapsed: 0.011 s
% 0.27/0.40 % (1097068)Peak memory usage: 10 MB
% 0.27/0.40 % (1097068)Instructions burned: 25 (million)
% 0.27/0.40 % (1097070)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=3293609226:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.27/0.40 % (1097069)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2888280619:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.27/0.40 % (1097076)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=289610646:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.27/0.40 % (1097076)Instruction limit reached!
% 0.27/0.40 % (1097076)------------------------------
% 0.27/0.40 % (1097076)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.27/0.40 % (1097076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/0.40 % (1097076)CaDiCaL version: 2.1.3
% 0.27/0.40 % (1097076)Termination reason: Instruction limit
% 0.27/0.40 % (1097076)Termination phase: shuffling
% 0.27/0.40 % (1097076)Time elapsed: 0.003 s
% 0.27/0.40 % (1097076)Peak memory usage: 10 MB
% 0.27/0.40 % (1097076)Instructions burned: 6 (million)
% 0.27/0.40 % (1097078)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.27/0.40 % (1097077)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3850419391:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.27/0.40 % (1097078)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=386153021:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.27/0.40 % (1097077)Instruction limit reached!
% 0.27/0.40 % (1097077)------------------------------
% 0.27/0.40 % (1097077)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.27/0.40 % (1097077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/0.40 % (1097077)CaDiCaL version: 2.1.3
% 0.27/0.40 % (1097077)Termination reason: Instruction limit
% 0.27/0.40 % (1097077)Termination phase: shuffling
% 0.27/0.40 % (1097077)Time elapsed: 0.003 s
% 0.27/0.40 % (1097077)Peak memory usage: 10 MB
% 0.27/0.40 % (1097077)Instructions burned: 6 (million)
% 0.27/0.40 % (1097078)Instruction limit reached!
% 0.27/0.40 % (1097078)------------------------------
% 0.27/0.40 % (1097078)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.27/0.40 % (1097078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/0.40 % (1097078)CaDiCaL version: 2.1.3
% 0.27/0.40 % (1097078)Termination reason: Instruction limit
% 0.27/0.40 % (1097078)Termination phase: shuffling
% 0.27/0.40 % (1097078)Time elapsed: 0.004 s
% 0.27/0.40 % (1097078)Peak memory usage: 10 MB
% 0.27/0.40 % (1097078)Instructions burned: 9 (million)
% 0.27/0.40 % (1097064)Instruction limit reached!
% 0.27/0.40 % (1097064)------------------------------
% 0.27/0.40 % (1097064)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.27/0.40 % (1097064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/0.40 % (1097064)CaDiCaL version: 2.1.3
% 0.27/0.40 % (1097064)Termination reason: Instruction limit
% 0.27/0.40 % (1097064)Termination phase: Property scanning
% 0.27/0.40 % (1097064)Time elapsed: 0.041 s
% 0.27/0.40 % (1097064)Peak memory usage: 12 MB
% 0.27/0.40 % (1097064)Instructions burned: 89 (million)
% 0.27/0.40 % (1097082)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2756513388:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.27/0.40 % (1097067) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1097059-1097067"...
% 0.27/0.40 % (1097085)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.27/0.40 % (1097085)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.27/0.40 % (1097067)...printing done.
% 0.27/0.40 % (1097067)Refutation found. Thanks to Tanya!
% 0.27/0.40 % SZS status Theorem for theBenchmark
% 0.27/0.40 % SZS output start Proof for theBenchmark
% 0.27/0.40 thf(type_def_5, type, product_prod: ($tType * $tType) > $tType).
% 0.27/0.40 thf(type_def_6, type, option: $tType > $tType).
% 0.27/0.40 thf(type_def_7, type, list: $tType > $tType).
% 0.27/0.40 thf(type_def_8, type, set: $tType > $tType).
% 0.27/0.40 thf(type_def_9, type, edgeD: $tType).
% 0.27/0.40 thf(type_def_10, type, node: $tType).
% 0.27/0.40 thf(type_def_11, type, var: $tType).
% 0.27/0.40 thf(type_def_12, type, val: $tType).
% 0.27/0.40 thf(type_def_13, type, g: $tType).
% 0.27/0.40 thf(type_def_14, type, sTfun: ($tType * $tType) > $tType).
% 0.27/0.40 thf(func_def_0, type, bounded_lattice_top: !>[X0: $tType]:($o)).
% 0.27/0.40 thf(func_def_1, type, bounded_lattice: !>[X0: $tType]:($o)).
% 0.27/0.40 thf(func_def_2, type, type: !>[X0: $tType]:($o)).
% 0.27/0.40 thf(func_def_3, type, sup: !>[X0: $tType]:($o)).
% 0.27/0.40 thf(func_def_4, type, order: !>[X0: $tType]:($o)).
% 0.27/0.40 thf(func_def_5, type, lattice: !>[X0: $tType]:($o)).
% 0.27/0.40 thf(func_def_6, type, finite_finite: !>[X0: $tType]:($o)).
% 0.27/0.40 thf(func_def_7, type, linorder: !>[X0: $tType]:($o)).
% 0.27/0.40 thf(func_def_8, type, preorder: !>[X0: $tType]:($o)).
% 0.27/0.40 thf(func_def_9, type, semilattice_sup: !>[X0: $tType]:($o)).
% 0.27/0.40 thf(func_def_10, type, bounde1808546759up_bot: !>[X0: $tType]:($o)).
% 0.27/0.40 thf(func_def_11, type, finite_finite2: !>[X0: $tType]:((set @ X0 > $o))).
% 0.27/0.40 thf(func_def_12, type, graph_1201503639essors: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > list @ product_prod @ X1 @ X2) > X0 > X1 > list @ X1))).
% 0.27/0.40 thf(func_def_13, type, graph_449533722essors: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > list @ X1) > (X0 > X1 > list @ product_prod @ X1 @ X2) > X0 > X1 > list @ X1))).
% 0.27/0.40 thf(func_def_14, type, irredu280805948_edges: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > list @ X1) > (X0 > X1 > set @ X2) > (X0 > product_prod @ X1 @ X2 > option @ list @ X2) > X0 > set @ X2 > set @ product_prod @ set @ X2 @ set @ X2))).
% 0.27/0.40 thf(func_def_15, type, irredu1918690039_nodes: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > list @ X1) > (X0 > X1 > set @ X2) > (X0 > product_prod @ X1 @ X2 > option @ list @ X2) > X0 > set @ X2 > set @ set @ X2))).
% 0.27/0.40 thf(func_def_16, type, irredu2110774547nt_scc: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > list @ X1) > (X0 > X1 > list @ product_prod @ X1 @ X2) > (X0 > X1 > set @ X3) > (X0 > X1 > set @ X3) > (X0 > product_prod @ X1 @ X3 > option @ list @ X3) > X0 > set @ X3 > set @ X3 > $o))).
% 0.27/0.40 thf(func_def_17, type, irredu2110905762nt_set: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > list @ X1) > (X0 > X1 > list @ product_prod @ X1 @ X2) > (X0 > X1 > set @ X3) > (X0 > X1 > set @ X3) > (X0 > product_prod @ X1 @ X3 > option @ list @ X3) > X0 > set @ X3 > $o))).
% 0.27/0.40 thf(func_def_18, type, sup_sup: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.27/0.40 thf(func_def_19, type, set2: !>[X0: $tType]:((list @ X0 > set @ X0))).
% 0.27/0.40 thf(func_def_20, type, zip: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > list @ product_prod @ X0 @ X1))).
% 0.27/0.40 thf(func_def_21, type, dom: !>[X0: $tType, X1: $tType]:(((X0 > option @ X1) > set @ X0))).
% 0.27/0.40 thf(func_def_22, type, none: !>[X0: $tType]:(option @ X0)).
% 0.27/0.40 thf(func_def_23, type, some: !>[X0: $tType]:((X0 > option @ X0))).
% 0.27/0.40 thf(func_def_24, type, bot_bot: !>[X0: $tType]:(X0)).
% 0.27/0.40 thf(func_def_25, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.27/0.40 thf(func_def_26, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.27/0.40 thf(func_def_27, type, sSA_CFG_SSA_allDefs: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > set @ X2) > (X0 > product_prod @ X1 @ X2 > option @ list @ X2) > X0 > X1 > set @ X2))).
% 0.27/0.40 thf(func_def_28, type, sSA_CFG_SSA_allUses: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > list @ X1) > (X0 > X1 > list @ product_prod @ X1 @ X2) > (X0 > X1 > set @ X3) > (X0 > product_prod @ X1 @ X3 > option @ list @ X3) > X0 > X1 > set @ X3))).
% 0.27/0.40 thf(func_def_29, type, sSA_CFG_SSA_allVars: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > list @ X1) > (X0 > X1 > list @ product_prod @ X1 @ X2) > (X0 > X1 > set @ X3) > (X0 > X1 > set @ X3) > (X0 > product_prod @ X1 @ X3 > option @ list @ X3) > X0 > set @ X3))).
% 0.27/0.40 thf(func_def_30, type, sSA_CFG_SSA_phiDefs: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > product_prod @ X1 @ X2 > option @ list @ X2) > X0 > X1 > set @ X2))).
% 0.27/0.40 thf(func_def_31, type, sSA_CFG_SSA_phiUses: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > list @ X1) > (X0 > X1 > list @ product_prod @ X1 @ X2) > (X0 > product_prod @ X1 @ X3 > option @ list @ X3) > X0 > X1 > set @ X3))).
% 0.27/0.40 thf(func_def_32, type, sSA_CF1081484811efNode: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > list @ X1) > (X0 > X1 > set @ X2) > (X0 > product_prod @ X1 @ X2 > option @ list @ X2) > X0 > X2 > X1))).
% 0.27/0.40 thf(func_def_33, type, sSA_CF1297404942ialPhi: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > list @ X1) > (X0 > X1 > set @ X2) > (X0 > product_prod @ X1 @ X2 > option @ list @ X2) > X0 > X2 > X2 > $o))).
% 0.27/0.40 thf(func_def_34, type, sSA_CF722422777iveVal: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > list @ X1) > (X0 > X1 > set @ X2) > (X0 > X1 > set @ X2) > (X0 > product_prod @ X1 @ X2 > option @ list @ X2) > X0 > X2 > $o))).
% 0.27/0.40 thf(func_def_35, type, sSA_CFG_SSA_wf_phi: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > list @ X1) > (X0 > X1 > set @ X2) > (X0 > product_prod @ X1 @ X2 > option @ list @ X2) > X0 > X2 > option @ list @ X2))).
% 0.27/0.40 thf(func_def_36, type, sSA_CF1165125185phiArg: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > list @ X1) > (X0 > X1 > set @ X2) > (X0 > product_prod @ X1 @ X2 > option @ list @ X2) > X0 > X2 > X2 > $o))).
% 0.27/0.40 thf(func_def_37, type, sSA_CF823892918pruned: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > list @ X1) > (X0 > X1 > set @ X2) > (X0 > X1 > set @ X2) > (X0 > product_prod @ X1 @ X2 > option @ list @ X2) > X0 > $o))).
% 0.27/0.40 thf(func_def_38, type, sSA_CF462202545undant: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > list @ X1) > (X0 > X1 > list @ product_prod @ X1 @ X2) > (X0 > X1 > set @ X3) > (X0 > X1 > set @ X3) > (X0 > product_prod @ X1 @ X3 > option @ list @ X3) > X0 > $o))).
% 0.27/0.40 thf(func_def_39, type, sSA_CF1363434349rivial: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > list @ X1) > (X0 > X1 > list @ product_prod @ X1 @ X2) > (X0 > X1 > set @ X3) > (X0 > X1 > set @ X3) > (X0 > product_prod @ X1 @ X3 > option @ list @ X3) > X0 > X3 > $o))).
% 0.27/0.40 thf(func_def_40, type, sSA_CFG_vars: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > list @ X1) > (X0 > X1 > set @ X2) > X0 > set @ X2))).
% 0.27/0.40 thf(func_def_41, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.27/0.40 thf(func_def_42, type, insert: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 0.27/0.40 thf(func_def_43, type, transitive_acyclic: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > $o))).
% 0.27/0.40 thf(func_def_44, type, transitive_tranclp: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > X0 > $o))).
% 0.27/0.40 thf(func_def_45, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.27/0.40 thf(func_def_46, type, alpha_n: (g > list @ node)).
% 0.27/0.40 thf(func_def_47, type, phi: val).
% 0.27/0.40 thf(func_def_48, type, phi_s: val).
% 0.27/0.40 thf(func_def_49, type, phi2: val).
% 0.27/0.40 thf(func_def_50, type, defs: (g > node > set @ val)).
% 0.27/0.40 thf(func_def_51, type, g2: g).
% 0.27/0.40 thf(func_def_52, type, inEdges: (g > node > list @ product_prod @ node @ edgeD)).
% 0.27/0.40 thf(func_def_53, type, phis: (g > product_prod @ node @ val > option @ list @ val)).
% 0.27/0.40 thf(func_def_54, type, s: val).
% 0.27/0.40 thf(func_def_55, type, uses: (g > node > set @ val)).
% 0.27/0.40 thf(func_def_56, type, var2: (g > val > var)).
% 0.27/0.40 thf(func_def_60, type, db0: !>[X0: $tType]:(X0)).
% 0.27/0.40 thf(func_def_61, type, db1: !>[X0: $tType]:(X0)).
% 0.27/0.40 thf(func_def_62, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.27/0.40 thf(func_def_63, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.27/0.40 thf(func_def_64, type, db2: !>[X0: $tType]:(X0)).
% 0.27/0.40 thf(func_def_65, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.27/0.40 thf(func_def_66, type, vAND: ($o > $o > $o)).
% 0.27/0.40 thf(func_def_67, type, db6: !>[X0: $tType]:(X0)).
% 0.27/0.40 thf(func_def_68, type, db5: !>[X0: $tType]:(X0)).
% 0.27/0.40 thf(func_def_69, type, db4: !>[X0: $tType]:(X0)).
% 0.27/0.40 thf(func_def_70, type, db3: !>[X0: $tType]:(X0)).
% 0.27/0.40 thf(func_def_71, type, vOR: ($o > $o > $o)).
% 0.27/0.40 thf(func_def_72, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.27/0.40 thf(func_def_73, type, vIMP: ($o > $o > $o)).
% 0.27/0.40 thf(func_def_74, type, db7: !>[X0: $tType]:(X0)).
% 0.27/0.40 thf(func_def_75, type, sK0: !>[X0: $tType]:((option @ X0 > X0))).
% 0.27/0.40 thf(func_def_76, type, sK1: !>[X0: $tType]:((set @ X0 > X0 > X0))).
% 0.27/0.40 thf(func_def_77, type, sK2: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.27/0.40 thf(func_def_78, type, sK3: !>[X0: $tType]:((set @ X0 > set @ X0 > (X0 > $o) > X0))).
% 0.27/0.40 thf(func_def_79, type, sK4: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.27/0.40 thf(func_def_80, type, sK5: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.27/0.40 thf(func_def_81, type, sK6: !>[X0: $tType]:((set @ X0 > set @ X0 > set @ X0 > set @ X0))).
% 0.27/0.40 thf(func_def_82, type, sK7: !>[X0: $tType]:((set @ X0 > set @ X0 > set @ X0 > set @ X0))).
% 0.27/0.40 thf(func_def_83, type, sK8: (set @ val > g > val)).
% 0.27/0.40 thf(func_def_84, type, sK9: (val > set @ val > g > val)).
% 0.27/0.40 thf(func_def_85, type, sK10: (val > set @ val > g > val)).
% 0.27/0.40 thf(func_def_86, type, sK11: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.27/0.40 thf(func_def_87, type, sK12: val).
% 0.27/0.40 thf(func_def_88, type, sK13: (g > node)).
% 0.27/0.40 thf(func_def_89, type, sK14: (g > val)).
% 0.27/0.40 thf(func_def_90, type, sK15: (set @ val > g > set @ val)).
% 0.27/0.40 thf(func_def_91, type, sK16: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.27/0.40 thf(func_def_92, type, sK17: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.27/0.40 thf(func_def_93, type, sK18: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.27/0.40 thf(func_def_94, type, sK19: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.27/0.40 thf(func_def_95, type, sK20: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.27/0.40 thf(func_def_96, type, sK21: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.27/0.40 thf(func_def_97, type, sK22: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.27/0.40 thf(func_def_98, type, sK23: (val > node > g > val)).
% 0.27/0.40 thf(func_def_99, type, sK24: !>[X0: $tType]:(((option @ X0 > $o) > X0))).
% 0.27/0.40 thf(func_def_100, type, sK25: (g > val)).
% 0.27/0.40 thf(func_def_101, type, sK26: (val > val > g > list @ val)).
% 0.27/0.40 thf(func_def_102, type, sK27: (val > g > node)).
% 0.27/0.40 thf(func_def_103, type, sK28: !>[X0: $tType]:((set @ X0 > list @ X0 > X0))).
% 0.27/0.40 thf(func_def_104, type, sK29: !>[X0: $tType]:((option @ X0 > X0))).
% 0.27/0.40 thf(func_def_105, type, sK30: !>[X0: $tType]:((set @ X0 > list @ X0))).
% 0.27/0.40 thf(func_def_106, type, sK31: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 0.27/0.40 thf(func_def_107, type, sK32: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.27/0.40 thf(func_def_108, type, sK33: !>[X0: $tType]:((set @ X0 > (X0 > $o) > set @ X0 > X0))).
% 0.27/0.40 thf(func_def_109, type, sK34: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0 > $o) > X1 > X0))).
% 0.27/0.40 thf(func_def_110, type, sK35: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0 > $o) > X1))).
% 0.27/0.40 thf(func_def_111, type, sK36: (val > g > val > node)).
% 0.27/0.40 thf(func_def_112, type, sK37: (g > val > node)).
% 0.27/0.40 thf(func_def_113, type, sK38: !>[X0: $tType]:((set @ X0 > X0))).
% 0.27/0.40 thf(func_def_114, type, sK39: (val > g > node > node)).
% 0.27/0.40 thf(func_def_115, type, sK40: (val > g > node > list @ val)).
% 0.27/0.40 thf(func_def_116, type, sK41: (val > g > node > val)).
% 0.27/0.40 thf(func_def_117, type, sK42: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.27/0.40 thf(func_def_118, type, sK43: !>[X0: $tType]:((set @ X0 > X0 > X0))).
% 0.27/0.40 thf(func_def_119, type, sK44: (list @ val > node > g > val)).
% 0.27/0.40 thf(func_def_120, type, sK45: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.27/0.40 thf(func_def_121, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > X0 > set @ X2) > X1 > (X1 > X0 > set @ X2) > (X2 > $o) > (X1 > product_prod @ X0 @ X2 > option @ list @ X2) > (X1 > list @ X0) > X2))).
% 0.27/0.40 thf(func_def_122, type, sK47: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > X0 > set @ X2) > X1 > (X1 > X0 > set @ X2) > (X2 > $o) > (X1 > product_prod @ X0 @ X2 > option @ list @ X2) > (X1 > list @ X0) > X2))).
% 0.27/0.40 thf(func_def_123, type, sK48: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > X0 > set @ X2) > X1 > (X2 > $o) > (X1 > list @ X0) > X2))).
% 0.27/0.40 thf(func_def_124, type, sK49: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > X0 > set @ X2) > X1 > (X2 > $o) > (X1 > list @ X0) > X0))).
% 0.27/0.40 thf(func_def_125, type, sK50: (g > val > node)).
% 0.27/0.40 thf(func_def_126, type, sK51: (g > val > val)).
% 0.27/0.40 thf(func_def_127, type, sK52: (g > val > val)).
% 0.27/0.40 thf(func_def_128, type, sK53: (g > val > val)).
% 0.27/0.40 thf(func_def_129, type, sK54: (g > val > node)).
% 0.27/0.40 thf(func_def_130, type, sK55: (g > val > val)).
% 0.27/0.40 thf(func_def_131, type, sK56: (set @ val > g > set @ val)).
% 0.27/0.40 thf(func_def_132, type, sK57: !>[X0: $tType]:((set @ X0 > X0))).
% 0.27/0.40 thf(func_def_133, type, sK58: !>[X0: $tType, X1: $tType]:((option @ X1 > option @ X0 > (option @ X0 > option @ X1 > $o) > X1))).
% 0.27/0.40 thf(func_def_134, type, sK59: !>[X0: $tType, X1: $tType]:((option @ X1 > option @ X0 > (option @ X0 > option @ X1 > $o) > X0))).
% 0.27/0.40 thf(func_def_135, type, sK60: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.27/0.40 thf(func_def_136, type, sK61: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > set @ X0) > X0 > X2 > (X2 > list @ X1) > X1))).
% 0.27/0.40 thf(func_def_137, type, sK62: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > set @ X0) > (X2 > product_prod @ X1 @ X0 > option @ list @ X0) > X0 > X2 > (X2 > X1 > set @ X0) > (X2 > list @ X1) > X0))).
% 0.27/0.40 thf(func_def_138, type, sK63: ((val > $o) > g > node)).
% 0.27/0.40 thf(func_def_139, type, sK64: ((val > $o) > g > val)).
% 0.27/0.40 thf(func_def_140, type, sK65: ((val > $o) > g > val)).
% 0.27/0.40 thf(func_def_141, type, sK66: ((val > $o) > g > val)).
% 0.27/0.40 thf(func_def_142, type, sK67: !>[X0: $tType]:((option @ X0 > X0))).
% 0.27/0.40 thf(func_def_143, type, sK68: (val > g > val)).
% 0.27/0.40 thf(func_def_144, type, sK69: (val > g > node)).
% 0.27/0.40 thf(func_def_145, type, vNOT: ($o > $o)).
% 0.27/0.40 thf(f3,axiom,(
% 0.27/0.40 (sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi2 @ phi_s)),
% 0.27/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__092_060open_062phiArg_Ag_A_092_060phi_062_H_A_092_060phi_062_092_060_094sub_062s_092_060close_062)).
% 0.27/0.40 thf(f7,axiom,(
% 0.27/0.40 ! [X1 : val,X2 : val,X0 : g] : ((sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ X0 @ X1 @ X2) => (member @ val @ X2 @ (sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ X0)))),
% 0.27/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_phiArg__in__allVars)).
% 0.27/0.40 thf(f301,conjecture,(
% 0.27/0.40 (member @ val @ phi_s @ (sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2))),
% 0.27/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.27/0.40 thf(f302,negated_conjecture,(
% 0.27/0.40 ~(member @ val @ phi_s @ (sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2))),
% 0.27/0.40 inference(negated_conjecture,[status(cth)],[f301])).
% 0.27/0.40 thf(f397,plain,(
% 0.27/0.40 ~(member @ val @ phi_s @ (sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2))),
% 0.27/0.40 inference(rectify,[],[f302])).
% 0.27/0.40 thf(f398,plain,(
% 0.27/0.40 ~ (((member @ val @ phi_s @ (sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2))) = $true)),
% 0.27/0.40 inference(fool_elimination,[],[f397])).
% 0.27/0.40 thf(f407,plain,(
% 0.27/0.40 ! [X0 : val,X1 : val,X2 : g] : ((sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ X2 @ X0 @ X1) => (member @ val @ X1 @ (sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ X2)))),
% 0.27/0.40 inference(rectify,[],[f7])).
% 0.27/0.40 thf(f408,plain,(
% 0.27/0.40 ! [X1 : val,X2 : g,X0 : val] : ((((sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ X2 @ X0 @ X1)) = $true) => (((member @ val @ X1 @ (sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ X2))) = $true))),
% 0.27/0.40 inference(fool_elimination,[],[f407])).
% 0.27/0.40 thf(f586,plain,(
% 0.27/0.40 (sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi2 @ phi_s)),
% 0.27/0.40 inference(rectify,[],[f3])).
% 0.27/0.40 thf(f587,plain,(
% 0.27/0.40 (((sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi2 @ phi_s)) = $true)),
% 0.27/0.40 inference(fool_elimination,[],[f586])).
% 0.27/0.40 thf(f851,plain,(
% 0.27/0.40 (((member @ val @ phi_s @ (sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2))) != $true)),
% 0.27/0.40 inference(flattening,[],[f398])).
% 0.27/0.40 thf(f956,plain,(
% 0.27/0.40 ! [X1 : val,X0 : val,X2 : g] : ((((member @ val @ X1 @ (sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ X2))) = $true) | (((sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ X2 @ X0 @ X1)) != $true))),
% 0.27/0.40 inference(ennf_transformation,[],[f408])).
% 0.27/0.40 thf(f1301,plain,(
% 0.27/0.40 ! [X0 : val,X1 : val,X2 : g] : (($true = ((member @ val @ X0 @ (sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ X2)))) | ($true != ((sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ X2 @ X1 @ X0))))),
% 0.27/0.40 inference(rectify,[],[f956])).
% 0.27/0.40 thf(f1630,plain,(
% 0.27/0.40 ( ! [X2 : g,X0 : val,X1 : val] : (($true = ((member @ val @ X0 @ (sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ X2)))) | ($true != ((sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ X2 @ X1 @ X0)))) )),
% 0.27/0.40 inference(cnf_transformation,[],[f1301])).
% 0.27/0.40 thf(f1771,plain,(
% 0.27/0.40 (((sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi2 @ phi_s)) = $true)),
% 0.27/0.40 inference(cnf_transformation,[],[f587])).
% 0.27/0.40 thf(f1863,plain,(
% 0.27/0.40 (((member @ val @ phi_s @ (sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2))) != $true)),
% 0.27/0.40 inference(cnf_transformation,[],[f851])).
% 0.27/0.40 thf(f1952,definition,(
% 0.27/0.40 spl70_9 <=> (((member @ val @ phi_s @ (sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2))) = $true)),
% 0.27/0.40 introduced(definition,[new_symbols(definition,[spl70_9])],[avatar_definition])).
% 0.27/0.40 thf(f1954,plain,(
% 0.27/0.40 (((member @ val @ phi_s @ (sSA_CFG_SSA_allVars @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2))) != $true) | spl70_9),
% 0.27/0.40 inference(avatar_component_clause,[],[f1952])).
% 0.27/0.40 thf(f1955,plain,(
% 0.27/0.40 ~spl70_9),
% 0.27/0.40 inference(avatar_split_clause,[],[f1863,f1952])).
% 0.27/0.40 thf(f1982,definition,(
% 0.27/0.40 spl70_15 <=> (((sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi2 @ phi_s)) = $true)),
% 0.27/0.40 introduced(definition,[new_symbols(definition,[spl70_15])],[avatar_definition])).
% 0.27/0.40 thf(f1984,plain,(
% 0.27/0.40 (((sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi2 @ phi_s)) = $true) | ~spl70_15),
% 0.27/0.40 inference(avatar_component_clause,[],[f1982])).
% 0.27/0.40 thf(f1985,plain,(
% 0.27/0.40 spl70_15),
% 0.27/0.40 inference(avatar_split_clause,[],[f1771,f1982])).
% 0.27/0.40 thf(f2108,plain,(
% 0.27/0.40 ( ! [X0 : val] : (($true != $true) | (((sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ X0 @ phi_s)) != $true)) ) | spl70_9),
% 0.27/0.40 inference(superposition,[],[f1954,f1630])).
% 0.27/0.40 thf(f2112,plain,(
% 0.27/0.40 ( ! [X0 : val] : ((((sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ X0 @ phi_s)) != $true)) ) | spl70_9),
% 0.27/0.40 inference(trivial_inequality_removal,[],[f2108])).
% 0.27/0.40 thf(f2179,plain,(
% 0.27/0.40 ($true != $true) | (spl70_9 | ~spl70_15)),
% 0.27/0.40 inference(superposition,[],[f2112,f1984])).
% 0.27/0.40 thf(f2180,plain,(
% 0.27/0.40 $false | (spl70_9 | ~spl70_15)),
% 0.27/0.40 inference(trivial_inequality_removal,[],[f2179])).
% 0.27/0.40 thf(f2181,plain,(
% 0.27/0.40 spl70_9 | ~spl70_15),
% 0.27/0.40 inference(avatar_contradiction_clause,[],[f2180])).
% 0.27/0.40 cnf(s10, plain, ~spl70_9, inference(sat_conversion,[],[f1955])).
% 0.27/0.40 cnf(s16, plain, spl70_15, inference(sat_conversion,[],[f1985])).
% 0.27/0.40 cnf(s37, plain, spl70_9 | ~spl70_15, inference(sat_conversion,[],[f2181])).
% 0.27/0.40 cnf(s40, plain, spl70_9, inference(rat,[],[s37,s16])).
% 0.27/0.40 cnf(s41, plain, $false, inference(rat,[],[s10,s40])).
% 0.27/0.40 thf(f2184,plain,(
% 0.27/0.40 $false),
% 0.27/0.40 inference(avatar_sat_refutation,[],[s41])).
% 0.27/0.40 % SZS output end Proof for theBenchmark
% 0.27/0.40 % (1097067)------------------------------
% 0.27/0.40 % (1097067)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.27/0.40 % (1097067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/0.40 % (1097067)CaDiCaL version: 2.1.3
% 0.27/0.40 % (1097067)Termination reason: Refutation
% 0.27/0.40 % (1097067)Time elapsed: 0.055 s
% 0.27/0.40 % (1097067)Peak memory usage: 15 MB
% 0.27/0.40 % (1097067)Instructions burned: 217 (million)
% 0.27/0.40 % (1097059)Success in time 0.102 s
% 0.27/0.40 % Vampire exiting
%------------------------------------------------------------------------------