%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM209^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 07:46:27 AM UTC 2026
% Result : Theorem 0.29s 0.38s
% Output : Refutation 0.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM209^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n017.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 17:48:52 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.22/0.28 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.29/0.38 % (671794)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.29/0.38 % (671802)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=892517181: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)
% 0.29/0.38 % (671800)lrs+10_16_si=on:nwc=1.5:random_seed=520421295:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.29/0.38 % (671799)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2286479232:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.29/0.38 % (671801)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1128758572:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.29/0.38 % (671803)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1004463751:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.29/0.38 % (671801)Instruction limit reached!
% 0.29/0.38 % (671801)------------------------------
% 0.29/0.38 % (671801)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.38 % (671801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.38 % (671801)CaDiCaL version: 2.1.3
% 0.29/0.38 % (671801)Termination reason: Instruction limit
% 0.29/0.38 % (671801)Termination phase: shuffling
% 0.29/0.38 % (671801)Time elapsed: 0.002 s
% 0.29/0.38 % (671801)Peak memory usage: 10 MB
% 0.29/0.38 % (671801)Instructions burned: 4 (million)
% 0.29/0.38 % (671800)Instruction limit reached!
% 0.29/0.38 % (671800)------------------------------
% 0.29/0.38 % (671800)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.38 % (671800)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.38 % (671800)CaDiCaL version: 2.1.3
% 0.29/0.38 % (671800)Termination reason: Instruction limit
% 0.29/0.38 % (671800)Termination phase: Property scanning
% 0.29/0.38 % (671800)Time elapsed: 0.009 s
% 0.29/0.38 % (671800)Peak memory usage: 10 MB
% 0.29/0.38 % (671800)Instructions burned: 19 (million)
% 0.29/0.38 % (671805)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.29/0.38 % (671805)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
% 0.29/0.38 % (671803)Instruction limit reached!
% 0.29/0.38 % (671803)------------------------------
% 0.29/0.38 % (671803)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.38 % (671803)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.38 % (671803)CaDiCaL version: 2.1.3
% 0.29/0.38 % (671803)Termination reason: Instruction limit
% 0.29/0.38 % (671803)Termination phase: Property scanning
% 0.29/0.38 % (671803)Time elapsed: 0.013 s
% 0.29/0.38 % (671803)Peak memory usage: 10 MB
% 0.29/0.38 % (671803)Instructions burned: 26 (million)
% 0.29/0.38 % (671805)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=2592702862:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.29/0.38 % (671804)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3839338956:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.29/0.38 % (671811)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3557608888:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.29/0.38 % (671811)Instruction limit reached!
% 0.29/0.38 % (671811)------------------------------
% 0.29/0.38 % (671811)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.38 % (671811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.38 % (671811)CaDiCaL version: 2.1.3
% 0.29/0.38 % (671811)Termination reason: Instruction limit
% 0.29/0.38 % (671811)Termination phase: shuffling
% 0.29/0.38 % (671811)Time elapsed: 0.002 s
% 0.29/0.38 % (671811)Peak memory usage: 10 MB
% 0.29/0.38 % (671811)Instructions burned: 3 (million)
% 0.29/0.38 % (671802) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-671794-671802"...
% 0.29/0.38 % (671812)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2720149848:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.29/0.38 % (671802)...printing done.
% 0.29/0.38 % (671813)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.29/0.38 % (671802)Refutation found. Thanks to Tanya!
% 0.29/0.38 % SZS status Theorem for theBenchmark
% 0.29/0.38 % SZS output start Proof for theBenchmark
% 0.29/0.38 thf(type_def_5, type, product_prod: ($tType * $tType) > $tType).
% 0.29/0.38 thf(type_def_6, type, sum_sum: ($tType * $tType) > $tType).
% 0.29/0.38 thf(type_def_7, type, dtree: $tType).
% 0.29/0.38 thf(type_def_8, type, set: $tType > $tType).
% 0.29/0.38 thf(type_def_9, type, t: $tType).
% 0.29/0.38 thf(type_def_10, type, itself: $tType > $tType).
% 0.29/0.38 thf(type_def_11, type, sTfun: ($tType * $tType) > $tType).
% 0.29/0.38 thf(func_def_0, type, bounded_lattice: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.29/0.38 thf(func_def_1, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.29/0.38 thf(func_def_2, type, lattice: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.29/0.38 thf(func_def_3, type, distrib_lattice: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.29/0.38 thf(func_def_4, type, semilattice_inf: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.29/0.38 thf(func_def_5, type, semilattice_sup: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.29/0.38 thf(func_def_6, type, bounded_lattice_top: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.29/0.38 thf(func_def_7, type, bounde1561333602nf_top: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.29/0.38 thf(func_def_8, type, bNF_Greatest_image2: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ X0 > (X0 > X1) > (X0 > X2) > set @ product_prod @ X1 @ X2))).
% 0.29/0.38 thf(func_def_9, type, cont: (dtree > set @ sum_sum @ t @ dtree)).
% 0.29/0.38 thf(func_def_10, type, comp: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > (X2 > X0) > X2 > X1))).
% 0.29/0.38 thf(func_def_11, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.29/0.38 thf(func_def_12, type, inf_inf: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.29/0.38 thf(func_def_13, type, sup_sup: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.29/0.38 thf(func_def_14, type, top_top: !>[X0: $tType]:(X0)).
% 0.29/0.38 thf(func_def_15, type, parall1899940088le_par: (product_prod @ dtree @ dtree > dtree)).
% 0.29/0.38 thf(func_def_16, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.29/0.38 thf(func_def_17, type, product_curry: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ X1 > X2) > X0 > X1 > X2))).
% 0.29/0.38 thf(func_def_18, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.29/0.38 thf(func_def_19, type, product_map_prod: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > X1) > (X2 > X3) > product_prod @ X0 @ X2 > product_prod @ X1 @ X3))).
% 0.29/0.38 thf(func_def_20, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.29/0.38 thf(func_def_21, type, product_case_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.29/0.38 thf(func_def_22, type, product_swap: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > product_prod @ X1 @ X0))).
% 0.29/0.38 thf(func_def_23, type, product_scomp: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > product_prod @ X1 @ X2) > (X1 > X2 > X3) > X0 > X3))).
% 0.29/0.38 thf(func_def_24, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.29/0.38 thf(func_def_25, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.29/0.38 thf(func_def_26, type, image: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1))).
% 0.29/0.38 thf(func_def_27, type, vimage: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X1 > set @ X0))).
% 0.29/0.38 thf(func_def_28, type, sum_Inl: !>[X0: $tType, X1: $tType]:((X0 > sum_sum @ X0 @ X1))).
% 0.29/0.38 thf(func_def_29, type, sum_Inr: !>[X0: $tType, X1: $tType]:((X0 > sum_sum @ X1 @ X0))).
% 0.29/0.38 thf(func_def_30, type, sum_Plus: !>[X0: $tType, X1: $tType]:((set @ X0 > set @ X1 > set @ sum_sum @ X0 @ X1))).
% 0.29/0.38 thf(func_def_31, type, sum_Suml: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > sum_sum @ X0 @ X2 > X1))).
% 0.29/0.38 thf(func_def_32, type, sum_Sumr: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > sum_sum @ X2 @ X0 > X1))).
% 0.29/0.38 thf(func_def_33, type, sum_rec_sum: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > (X2 > X1) > sum_sum @ X0 @ X2 > X1))).
% 0.29/0.38 thf(func_def_34, type, sum_case_sum: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > (X2 > X1) > sum_sum @ X0 @ X2 > X1))).
% 0.29/0.38 thf(func_def_35, type, type_definition: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > set @ X1 > $o))).
% 0.29/0.38 thf(func_def_36, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.29/0.38 thf(func_def_37, type, tr1: dtree).
% 0.29/0.38 thf(func_def_38, type, tr1a: dtree).
% 0.29/0.38 thf(func_def_39, type, tr2: dtree).
% 0.29/0.38 thf(func_def_40, type, tr2a: dtree).
% 0.29/0.38 thf(func_def_41, type, tr3: dtree).
% 0.29/0.38 thf(func_def_42, type, tr3a: dtree).
% 0.29/0.38 thf(func_def_43, type, trA: dtree).
% 0.29/0.38 thf(func_def_44, type, trA2: dtree).
% 0.29/0.38 thf(func_def_45, type, trB: dtree).
% 0.29/0.38 thf(func_def_49, type, db2: !>[X0: $tType]:(X0)).
% 0.29/0.38 thf(func_def_50, type, db0: !>[X0: $tType]:(X0)).
% 0.29/0.38 thf(func_def_51, type, db1: !>[X0: $tType]:(X0)).
% 0.29/0.38 thf(func_def_52, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.29/0.38 thf(func_def_53, type, vAND: ($o > $o > $o)).
% 0.29/0.38 thf(func_def_54, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.29/0.38 thf(func_def_55, type, vOR: ($o > $o > $o)).
% 0.29/0.38 thf(func_def_56, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.29/0.38 thf(func_def_57, type, sK0: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X1))).
% 0.29/0.38 thf(func_def_58, type, sK1: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X0))).
% 0.29/0.38 thf(func_def_59, type, sK2: !>[X0: $tType, X1: $tType]:((sum_sum @ X0 @ X1 > X1))).
% 0.29/0.38 thf(func_def_60, type, sK3: !>[X0: $tType, X1: $tType]:((sum_sum @ X0 @ X1 > X0))).
% 0.29/0.38 thf(func_def_61, type, sK4: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > (X0 > X1) > X0))).
% 0.29/0.38 thf(func_def_62, type, sK5: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X0))).
% 0.29/0.38 thf(func_def_63, type, sK6: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X1))).
% 0.29/0.38 thf(func_def_64, type, sK7: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ X2 > $o) > X2))).
% 0.29/0.38 thf(func_def_65, type, sK8: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ X2 > $o) > X0))).
% 0.29/0.38 thf(func_def_66, type, sK9: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ X2 > $o) > X1))).
% 0.29/0.38 thf(func_def_67, type, sK10: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ X1 > X0 > (X2 > X1 > set @ X0) > X2))).
% 0.29/0.38 thf(func_def_68, type, sK11: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ X1 > X0 > (X2 > X1 > set @ X0) > X1))).
% 0.29/0.38 thf(func_def_69, type, sK12: !>[X0: $tType, X1: $tType]:((sum_sum @ X1 @ X0 > X0))).
% 0.29/0.38 thf(func_def_70, type, sK13: !>[X0: $tType, X1: $tType]:((sum_sum @ X1 @ X0 > X1))).
% 0.29/0.38 thf(func_def_71, type, sK14: !>[X0: $tType, X1: $tType]:((sum_sum @ X0 @ X1 > X0))).
% 0.29/0.38 thf(func_def_72, type, sK15: !>[X0: $tType, X1: $tType]:((sum_sum @ X0 @ X1 > X1))).
% 0.29/0.38 thf(func_def_73, type, sK16: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X0 @ X1 > $o) > X1))).
% 0.29/0.38 thf(func_def_74, type, sK17: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X0 @ X1 > $o) > X4))).
% 0.29/0.38 thf(func_def_75, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X0 @ X1 > $o) > X3))).
% 0.29/0.38 thf(func_def_76, type, sK19: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X0 @ X1 > $o) > X2))).
% 0.29/0.38 thf(func_def_77, type, sK20: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X0 @ X1 > $o) > X0))).
% 0.29/0.38 thf(func_def_78, type, sK21: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > X0) > X1))).
% 0.29/0.38 thf(func_def_79, type, sK22: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.29/0.38 thf(func_def_80, type, sK23: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > (X0 > X1) > X0))).
% 0.29/0.38 thf(func_def_81, type, sK24: !>[X0: $tType, X1: $tType]:(((sum_sum @ X1 @ X0 > $o) > X0))).
% 0.29/0.38 thf(func_def_82, type, sK25: !>[X0: $tType, X1: $tType]:(((sum_sum @ X1 @ X0 > $o) > X1))).
% 0.29/0.38 thf(func_def_83, type, sK26: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X2 @ X1 > X1))).
% 0.29/0.38 thf(func_def_84, type, sK27: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X2 @ X1 > X2))).
% 0.29/0.38 thf(func_def_85, type, sK28: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X2 @ X1 > X3))).
% 0.29/0.38 thf(func_def_86, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X2 @ X1 > X0))).
% 0.29/0.38 thf(func_def_87, type, sK30: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 0.29/0.38 thf(func_def_88, type, sK31: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 0.29/0.38 thf(func_def_89, type, sK32: !>[X0: $tType]:(((X0 > $o) > set @ X0 > set @ X0 > X0))).
% 0.29/0.38 thf(func_def_90, type, sK33: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 0.29/0.38 thf(func_def_91, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X0 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X3 @ X2 > $o) > X5))).
% 0.29/0.38 thf(func_def_92, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X0 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X3 @ X2 > $o) > X1))).
% 0.29/0.38 thf(func_def_93, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X0 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X3 @ X2 > $o) > X4))).
% 0.29/0.38 thf(func_def_94, type, sK37: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X0 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X3 @ X2 > $o) > X0))).
% 0.29/0.38 thf(func_def_95, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X0 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X3 @ X2 > $o) > X2))).
% 0.29/0.38 thf(func_def_96, type, sK39: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X0 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X3 @ X2 > $o) > X3))).
% 0.29/0.38 thf(func_def_97, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > (X0 > X2 > X1) > (X0 > X2 > X1) > X2))).
% 0.29/0.38 thf(func_def_98, type, sK41: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > (X0 > X2 > X1) > (X0 > X2 > X1) > X0))).
% 0.29/0.38 thf(func_def_99, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2) > (X0 > X2) > (X1 > X0) > (X1 > X0) > X0))).
% 0.29/0.38 thf(func_def_100, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2) > (X0 > X2) > (X1 > X0) > (X1 > X0) > X0))).
% 0.29/0.38 thf(func_def_101, type, sK44: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X0 > X1))).
% 0.29/0.38 thf(func_def_102, type, sK45: !>[X0: $tType]:((set @ X0 > set @ X0 > (X0 > $o) > X0))).
% 0.29/0.38 thf(func_def_103, type, sK46: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.29/0.38 thf(func_def_104, type, sK47: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.29/0.38 thf(func_def_105, type, sK48: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X0) > (X1 > X2) > (X2 > X0) > X2))).
% 0.29/0.38 thf(func_def_106, type, sK49: dtree).
% 0.29/0.38 thf(func_def_107, type, sK50: dtree).
% 0.29/0.38 thf(func_def_108, type, sK51: dtree).
% 0.29/0.38 thf(func_def_109, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X6 @ X3 > X2))).
% 0.29/0.38 thf(func_def_110, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X6 @ X3 > X6))).
% 0.29/0.38 thf(func_def_111, type, sK54: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X6 @ X3 > X4))).
% 0.29/0.38 thf(func_def_112, type, sK55: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X6 @ X3 > X3))).
% 0.29/0.38 thf(func_def_113, type, sK56: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X6 @ X3 > X1))).
% 0.29/0.38 thf(func_def_114, type, sK57: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X6 @ X3 > X5))).
% 0.29/0.38 thf(func_def_115, type, sK58: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X6 @ X3 > X0))).
% 0.29/0.38 thf(func_def_116, type, sK59: !>[X0: $tType, X1: $tType]:(((X1 > $o) > set @ X0 > (X0 > X1) > X1))).
% 0.29/0.38 thf(func_def_117, type, sK60: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X0) > (X0 > X1) > (X0 > X1) > X0))).
% 0.29/0.38 thf(func_def_118, type, sK61: !>[X0: $tType, X1: $tType]:((set @ X0 > sum_sum @ X0 @ X1 > X0))).
% 0.29/0.38 thf(func_def_119, type, sK62: !>[X0: $tType, X1: $tType]:((set @ X1 > sum_sum @ X0 @ X1 > X1))).
% 0.29/0.38 thf(func_def_120, type, sK63: (product_prod @ dtree @ dtree > dtree)).
% 0.29/0.38 thf(func_def_121, type, sK64: (product_prod @ dtree @ dtree > dtree)).
% 0.29/0.38 thf(func_def_122, type, sK65: !>[X0: $tType]:(X0)).
% 0.29/0.38 thf(func_def_123, type, sK66: !>[X0: $tType]:(X0)).
% 0.29/0.38 thf(func_def_124, type, sK67: !>[X0: $tType]:(X0)).
% 0.29/0.38 thf(func_def_125, type, sK68: !>[X0: $tType, X1: $tType, X2: $tType]:(($o > (sum_sum @ X1 @ X2 > X0) > X0 > X2))).
% 0.29/0.38 thf(func_def_126, type, sK69: !>[X0: $tType, X1: $tType, X2: $tType]:(($o > (sum_sum @ X1 @ X2 > X0) > X0 > X1))).
% 0.29/0.38 thf(func_def_127, type, sK70: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 0.29/0.38 thf(func_def_128, type, sK71: !>[X0: $tType]:(X0)).
% 0.29/0.38 thf(func_def_129, type, sK72: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X0) > (X1 > X2) > (X2 > X0) > set @ X1 > X1))).
% 0.29/0.38 thf(func_def_130, type, sK73: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0))).
% 0.29/0.38 thf(func_def_131, type, sK74: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X1))).
% 0.29/0.38 thf(func_def_132, type, sK75: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > $o) > (X0 > $o) > X1))).
% 0.29/0.38 thf(func_def_133, type, sK76: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X1 @ product_prod @ X0 @ X2 > X0))).
% 0.29/0.38 thf(func_def_134, type, sK77: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X1 @ product_prod @ X0 @ X2 > X2))).
% 0.29/0.38 thf(func_def_135, type, sK78: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X1 @ product_prod @ X0 @ X2 > X1))).
% 0.29/0.38 thf(func_def_136, type, sK79: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X0))).
% 0.29/0.38 thf(func_def_137, type, sK80: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 0.29/0.38 thf(func_def_138, type, sK81: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > (X1 > X0) > X1))).
% 0.29/0.38 thf(func_def_139, type, sK82: !>[X0: $tType]:(X0)).
% 0.29/0.38 thf(func_def_140, type, sK83: !>[X0: $tType]:(X0)).
% 0.29/0.38 thf(func_def_141, type, sK84: !>[X0: $tType]:(X0)).
% 0.29/0.38 thf(func_def_142, type, sK85: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ X1 @ X2 > (X1 > X3) > (X2 > X0) > product_prod @ X3 @ X0 > X1))).
% 0.29/0.38 thf(func_def_143, type, sK86: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ X1 @ X2 > (X1 > X3) > (X2 > X0) > product_prod @ X3 @ X0 > X2))).
% 0.29/0.38 thf(func_def_144, type, sK87: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ X4 > X1))).
% 0.29/0.38 thf(func_def_145, type, sK88: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ X4 > X2))).
% 0.29/0.38 thf(func_def_146, type, sK89: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ X4 > X0))).
% 0.29/0.38 thf(func_def_147, type, sK90: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ X4 > X4))).
% 0.29/0.38 thf(func_def_148, type, sK91: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ X4 > X3))).
% 0.29/0.38 thf(func_def_149, type, sK92: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X2 @ X3 > $o) > X0))).
% 0.29/0.38 thf(func_def_150, type, sK93: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X2 @ X3 > $o) > X5))).
% 0.29/0.38 thf(func_def_151, type, sK94: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X2 @ X3 > $o) > X3))).
% 0.29/0.38 thf(func_def_152, type, sK95: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X2 @ X3 > $o) > X1))).
% 0.29/0.38 thf(func_def_153, type, sK96: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X2 @ X3 > $o) > X2))).
% 0.29/0.38 thf(func_def_154, type, sK97: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X2 @ X3 > $o) > X4))).
% 0.29/0.38 thf(func_def_155, type, sK98: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X2 @ X3 > $o) > X6))).
% 0.29/0.38 thf(func_def_156, type, sK99: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > X1))).
% 0.29/0.38 thf(func_def_157, type, sK100: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X1))).
% 0.29/0.38 thf(func_def_158, type, sK101: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0))).
% 0.29/0.38 thf(func_def_159, type, sK102: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X4 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ X2 > X4))).
% 0.29/0.38 thf(func_def_160, type, sK103: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X4 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ X2 > X0))).
% 0.29/0.38 thf(func_def_161, type, sK104: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X4 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ X2 > X2))).
% 0.29/0.38 thf(func_def_162, type, sK105: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X4 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ X2 > X5))).
% 0.29/0.38 thf(func_def_163, type, sK106: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X4 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ X2 > X1))).
% 0.29/0.38 thf(func_def_164, type, sK107: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X4 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ X2 > X3))).
% 0.29/0.38 thf(func_def_165, type, sK108: !>[X0: $tType]:((set @ X0 > X0))).
% 0.29/0.38 thf(func_def_166, type, sK109: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X0 > X1))).
% 0.29/0.38 thf(func_def_167, type, sK110: dtree).
% 0.29/0.38 thf(func_def_168, type, sK111: dtree).
% 0.29/0.38 thf(func_def_169, type, sK112: dtree).
% 0.29/0.38 thf(func_def_170, type, sK113: ((product_prod @ dtree @ dtree > $o) > dtree)).
% 0.29/0.38 thf(func_def_171, type, sK114: ((product_prod @ dtree @ dtree > $o) > dtree)).
% 0.29/0.38 thf(func_def_172, type, sK115: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > $o) > X1))).
% 0.29/0.38 thf(func_def_173, type, sK116: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > $o) > X2))).
% 0.29/0.38 thf(func_def_174, type, sK117: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > $o) > X3))).
% 0.29/0.38 thf(func_def_175, type, sK118: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > $o) > X0))).
% 0.29/0.38 thf(func_def_176, type, sK119: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.29/0.38 thf(func_def_177, type, sK120: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X1 > X0))).
% 0.29/0.38 thf(func_def_178, type, vNOT: ($o > $o)).
% 0.29/0.38 thf(f5,axiom,(
% 0.29/0.38 (trA = ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ (parall1899940088le_par @ (product_Pair @ dtree @ dtree @ tr1 @ tr2)) @ tr3))))),
% 0.29/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__092_060open_062trA_H_A_061_A_Itr1_H_A_092_060parallel_062_Atr2_H_J_A_092_060parallel_062_Atr3_H_092_060close_062)).
% 0.29/0.38 thf(f285,conjecture,(
% 0.29/0.38 ? [X1 : dtree,X0 : dtree,X2 : dtree] : ((((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ tr1 @ (parall1899940088le_par @ (product_Pair @ dtree @ dtree @ tr2 @ tr3))))) = ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X0 @ (parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X1 @ X2)))))) & (trA = ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ (parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X0 @ X1)) @ X2)))))),
% 0.29/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4)).
% 0.29/0.38 thf(f286,negated_conjecture,(
% 0.29/0.38 ~ ? [X1 : dtree,X0 : dtree,X2 : dtree] : ((((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ tr1 @ (parall1899940088le_par @ (product_Pair @ dtree @ dtree @ tr2 @ tr3))))) = ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X0 @ (parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X1 @ X2)))))) & (trA = ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ (parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X0 @ X1)) @ X2)))))),
% 0.29/0.38 inference(negated_conjecture,[status(cth)],[f285])).
% 0.29/0.38 thf(f671,plain,(
% 0.29/0.38 ~ ? [X1 : dtree,X0 : dtree,X2 : dtree] : ((((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ tr1 @ (parall1899940088le_par @ (product_Pair @ dtree @ dtree @ tr2 @ tr3))))) = ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X1 @ (parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X0 @ X2)))))) & (trA = ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ (parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X1 @ X0)) @ X2)))))),
% 0.29/0.38 inference(rectify,[],[f286])).
% 0.29/0.38 thf(f863,plain,(
% 0.29/0.38 ! [X0 : dtree,X2 : dtree,X1 : dtree] : ((((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ tr1 @ (parall1899940088le_par @ (product_Pair @ dtree @ dtree @ tr2 @ tr3))))) != ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X1 @ (parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X0 @ X2)))))) | (trA != ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ (parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X1 @ X0)) @ X2)))))),
% 0.29/0.38 inference(ennf_transformation,[],[f671])).
% 0.29/0.38 thf(f1124,plain,(
% 0.29/0.38 ! [X0 : dtree,X1 : dtree,X2 : dtree] : ((((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ tr1 @ (parall1899940088le_par @ (product_Pair @ dtree @ dtree @ tr2 @ tr3))))) != ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X2 @ (parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X0 @ X1)))))) | (trA != ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ (parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X2 @ X0)) @ X1)))))),
% 0.29/0.38 inference(rectify,[],[f863])).
% 0.29/0.38 thf(f1268,plain,(
% 0.29/0.38 (trA = ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ (parall1899940088le_par @ (product_Pair @ dtree @ dtree @ tr1 @ tr2)) @ tr3))))),
% 0.29/0.38 inference(cnf_transformation,[],[f5])).
% 0.29/0.38 thf(f1464,plain,(
% 0.29/0.38 ( ! [X2 : dtree,X0 : dtree,X1 : dtree] : ((((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ tr1 @ (parall1899940088le_par @ (product_Pair @ dtree @ dtree @ tr2 @ tr3))))) != ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X2 @ (parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X0 @ X1)))))) | (trA != ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ (parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X2 @ X0)) @ X1))))) )),
% 0.29/0.38 inference(cnf_transformation,[],[f1124])).
% 0.29/0.38 thf(f1632,definition,(
% 0.29/0.38 spl121_10 <=> (trA = ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ (parall1899940088le_par @ (product_Pair @ dtree @ dtree @ tr1 @ tr2)) @ tr3))))),
% 0.29/0.38 introduced(definition,[new_symbols(definition,[spl121_10])],[avatar_definition])).
% 0.29/0.38 thf(f1635,plain,(
% 0.29/0.38 spl121_10),
% 0.29/0.38 inference(avatar_split_clause,[],[f1268,f1632])).
% 0.29/0.38 thf(f1679,plain,(
% 0.29/0.38 (trA != ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ (parall1899940088le_par @ (product_Pair @ dtree @ dtree @ tr1 @ tr2)) @ tr3))))),
% 0.29/0.38 inference(equality_resolution,[],[f1464])).
% 0.29/0.38 thf(f1680,plain,(
% 0.29/0.38 ~spl121_10),
% 0.29/0.38 inference(avatar_split_clause,[],[f1679,f1632])).
% 0.29/0.38 cnf(s10, plain, spl121_10, inference(sat_conversion,[],[f1635])).
% 0.29/0.38 cnf(s19, plain, ~spl121_10, inference(sat_conversion,[],[f1680])).
% 0.29/0.38 cnf(s20, plain, $false, inference(rat,[],[s10,s19])).
% 0.29/0.38 thf(f1681,plain,(
% 0.29/0.38 $false),
% 0.29/0.38 inference(avatar_sat_refutation,[],[s20])).
% 0.29/0.38 % SZS output end Proof for theBenchmark
% 0.29/0.38 % (671802)------------------------------
% 0.29/0.38 % (671802)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.38 % (671802)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.38 % (671802)CaDiCaL version: 2.1.3
% 0.29/0.38 % (671802)Termination reason: Refutation
% 0.29/0.38 % (671802)Time elapsed: 0.035 s
% 0.29/0.38 % (671802)Peak memory usage: 14 MB
% 0.29/0.38 % (671802)Instructions burned: 124 (million)
% 0.29/0.38 % (671794)Success in time 0.088 s
% 0.29/0.38 % Vampire exiting
%------------------------------------------------------------------------------