%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP107^2 : 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 : n002.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 08:08:22 AM UTC 2026
% Result : Theorem 0.22s 0.36s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP107^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n002.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 19:57:08 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.26 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
% 0.22/0.36 % (1769068)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.36 % (1769076)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=533065091: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)
% 0.22/0.36 % (1769079)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.36 % (1769079)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
% 0.22/0.36 % (1769074)lrs+10_16_si=on:nwc=1.5:random_seed=1200361557:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.36 % (1769073)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=999529605:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.36 % (1769075)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=167887240:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.36 % (1769077)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3997569980:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.36 % (1769079)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=3493987722:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.36 % (1769075)Instruction limit reached!
% 0.22/0.36 % (1769075)------------------------------
% 0.22/0.36 % (1769075)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (1769075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (1769075)CaDiCaL version: 2.1.3
% 0.22/0.36 % (1769075)Termination reason: Instruction limit
% 0.22/0.36 % (1769075)Termination phase: shuffling
% 0.22/0.36 % (1769075)Time elapsed: 0.002 s
% 0.22/0.36 % (1769075)Peak memory usage: 10 MB
% 0.22/0.36 % (1769075)Instructions burned: 3 (million)
% 0.22/0.36 % (1769074)Instruction limit reached!
% 0.22/0.36 % (1769074)------------------------------
% 0.22/0.36 % (1769074)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (1769074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (1769074)CaDiCaL version: 2.1.3
% 0.22/0.36 % (1769074)Termination reason: Instruction limit
% 0.22/0.36 % (1769074)Termination phase: shuffling
% 0.22/0.36 % (1769074)Time elapsed: 0.009 s
% 0.22/0.36 % (1769074)Peak memory usage: 10 MB
% 0.22/0.36 % (1769074)Instructions burned: 20 (million)
% 0.22/0.36 % (1769077)Instruction limit reached!
% 0.22/0.36 % (1769077)------------------------------
% 0.22/0.36 % (1769077)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (1769077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (1769077)CaDiCaL version: 2.1.3
% 0.22/0.36 % (1769077)Termination reason: Instruction limit
% 0.22/0.36 % (1769077)Termination phase: shuffling
% 0.22/0.36 % (1769077)Time elapsed: 0.011 s
% 0.22/0.36 % (1769077)Peak memory usage: 10 MB
% 0.22/0.36 % (1769077)Instructions burned: 25 (million)
% 0.22/0.36 % (1769078)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=511679573:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.36 % (1769086)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3526135238:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.36 % (1769086)Instruction limit reached!
% 0.22/0.36 % (1769086)------------------------------
% 0.22/0.36 % (1769086)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (1769086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (1769086)CaDiCaL version: 2.1.3
% 0.22/0.36 % (1769086)Termination reason: Instruction limit
% 0.22/0.36 % (1769086)Termination phase: shuffling
% 0.22/0.36 % (1769086)Time elapsed: 0.003 s
% 0.22/0.36 % (1769086)Peak memory usage: 10 MB
% 0.22/0.36 % (1769086)Instructions burned: 6 (million)
% 0.22/0.36 % (1769088)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.36 % (1769087)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1805459292:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.22/0.36 % (1769088)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=434981217:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.22/0.36 % (1769087)Instruction limit reached!
% 0.22/0.36 % (1769087)------------------------------
% 0.22/0.36 % (1769087)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (1769087)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (1769087)CaDiCaL version: 2.1.3
% 0.22/0.36 % (1769087)Termination reason: Instruction limit
% 0.22/0.36 % (1769087)Termination phase: shuffling
% 0.22/0.36 % (1769087)Time elapsed: 0.003 s
% 0.22/0.36 % (1769087)Peak memory usage: 10 MB
% 0.22/0.36 % (1769087)Instructions burned: 6 (million)
% 0.22/0.36 % (1769076) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1769068-1769076"...
% 0.22/0.36 % (1769088)Instruction limit reached!
% 0.22/0.36 % (1769088)------------------------------
% 0.22/0.36 % (1769088)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (1769088)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (1769088)CaDiCaL version: 2.1.3
% 0.22/0.36 % (1769088)Termination reason: Instruction limit
% 0.22/0.36 % (1769088)Termination phase: shuffling
% 0.22/0.36 % (1769088)Time elapsed: 0.004 s
% 0.22/0.36 % (1769088)Peak memory usage: 10 MB
% 0.22/0.36 % (1769088)Instructions burned: 7 (million)
% 0.22/0.36 % (1769076)...printing done.
% 0.22/0.36 % (1769076)Refutation found. Thanks to Tanya!
% 0.22/0.36 % SZS status Theorem for theBenchmark
% 0.22/0.36 % SZS output start Proof for theBenchmark
% 0.22/0.36 thf(type_def_5, type, partia1265057091ct_ext: ($tType * $tType) > $tType).
% 0.22/0.36 thf(type_def_6, type, eq_eq_object_ext: ($tType * $tType) > $tType).
% 0.22/0.36 thf(type_def_7, type, monoid_ext: ($tType * $tType) > $tType).
% 0.22/0.36 thf(type_def_8, type, ring_ext: ($tType * $tType) > $tType).
% 0.22/0.36 thf(type_def_9, type, product_unit: $tType).
% 0.22/0.36 thf(type_def_10, type, product_prod: ($tType * $tType) > $tType).
% 0.22/0.36 thf(type_def_11, type, set: $tType > $tType).
% 0.22/0.36 thf(type_def_12, type, nat: $tType).
% 0.22/0.36 thf(type_def_13, type, int: $tType).
% 0.22/0.36 thf(type_def_14, type, b: $tType).
% 0.22/0.36 thf(type_def_15, type, a: $tType).
% 0.22/0.36 thf(type_def_16, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.36 thf(func_def_0, type, a_RCOSETS: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > set @ X0 > set @ set @ X0))).
% 0.22/0.36 thf(func_def_1, type, a_l_coset: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > X0 > set @ X0 > set @ X0))).
% 0.22/0.36 thf(func_def_2, type, a_r_coset: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > set @ X0 > X0 > set @ X0))).
% 0.22/0.36 thf(func_def_3, type, additive_subgroup: !>[X0: $tType, X1: $tType]:((set @ X0 > partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > $o))).
% 0.22/0.36 thf(func_def_4, type, set_add: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > set @ X0 > set @ X0 > set @ X0))).
% 0.22/0.36 thf(func_def_5, type, equivalence: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ eq_eq_object_ext @ X0 @ X1 > $o))).
% 0.22/0.36 thf(func_def_6, type, partial_carrier: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ X1 > set @ X0))).
% 0.22/0.36 thf(func_def_7, type, units: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ X1 > set @ X0))).
% 0.22/0.36 thf(func_def_8, type, group: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ X1 > $o))).
% 0.22/0.36 thf(func_def_9, type, monoid: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ X1 > $o))).
% 0.22/0.36 thf(func_def_10, type, mult: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ X1 > X0 > X0 > X0))).
% 0.22/0.36 thf(func_def_11, type, one: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ X1 > X0))).
% 0.22/0.36 thf(func_def_12, type, units_of: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ X1 > partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ product_unit))).
% 0.22/0.36 thf(func_def_13, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.22/0.36 thf(func_def_14, type, locali1641774487f_frac: !>[X0: $tType, X1: $tType, X2: $tType]:((partia1265057091ct_ext @ product_prod @ X0 @ X1 @ eq_eq_object_ext @ product_prod @ X0 @ X1 @ X2 > X0 > X1 > set @ product_prod @ X0 @ X1))).
% 0.22/0.36 thf(func_def_15, type, locali1648044335f_frac: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > set @ X0 > $o))).
% 0.22/0.36 thf(func_def_16, type, locali1768110497f_frac: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > set @ X0 > partia1265057091ct_ext @ set @ product_prod @ X0 @ X0 @ monoid_ext @ set @ product_prod @ X0 @ X0 @ product_unit))).
% 0.22/0.36 thf(func_def_17, type, locali7914339f_crng: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > set @ X0 > $o))).
% 0.22/0.36 thf(func_def_18, type, locali1402578320of_rng: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > set @ X0 > $o))).
% 0.22/0.36 thf(func_def_19, type, locali990921413f_frac: !>[X0: $tType, X1: $tType, X2: $tType]:((partia1265057091ct_ext @ product_prod @ X0 @ X1 @ eq_eq_object_ext @ product_prod @ X0 @ X1 @ X2 > set @ set @ product_prod @ X0 @ X1))).
% 0.22/0.36 thf(func_def_20, type, locali1441642228monoid: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ X1 > set @ X0 > $o))).
% 0.22/0.36 thf(func_def_21, type, bot_bot: !>[X0: $tType]:(X0)).
% 0.22/0.36 thf(func_def_22, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.36 thf(func_def_23, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.22/0.36 thf(func_def_24, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.22/0.36 thf(func_def_25, type, abelian_monoid: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > $o))).
% 0.22/0.36 thf(func_def_26, type, add_pow: !>[X0: $tType, X1: $tType, X2: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > X2 > X0 > X0))).
% 0.22/0.36 thf(func_def_27, type, field: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > $o))).
% 0.22/0.36 thf(func_def_28, type, ring: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > $o))).
% 0.22/0.36 thf(func_def_29, type, zero: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > X0))).
% 0.22/0.36 thf(func_def_30, type, semiring: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > $o))).
% 0.22/0.36 thf(func_def_31, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.22/0.36 thf(func_def_32, type, pow: !>[X0: $tType]:((set @ X0 > set @ set @ X0))).
% 0.22/0.36 thf(func_def_33, type, insert: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 0.22/0.36 thf(func_def_34, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.22/0.36 thf(func_def_35, type, r: partia1265057091ct_ext @ a @ monoid_ext @ a @ ring_ext @ a @ b).
% 0.22/0.36 thf(func_def_36, type, s: set @ a).
% 0.22/0.36 thf(func_def_37, type, r2: a).
% 0.22/0.36 thf(func_def_38, type, r3: a).
% 0.22/0.36 thf(func_def_39, type, rel: partia1265057091ct_ext @ product_prod @ a @ a @ eq_eq_object_ext @ product_prod @ a @ a @ product_unit).
% 0.22/0.36 thf(func_def_40, type, s2: a).
% 0.22/0.36 thf(func_def_41, type, s3: a).
% 0.22/0.36 thf(func_def_45, type, vAND: ($o > $o > $o)).
% 0.22/0.36 thf(func_def_46, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.36 thf(func_def_47, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.36 thf(func_def_48, type, vIMP: ($o > $o > $o)).
% 0.22/0.36 thf(func_def_49, type, db2: !>[X0: $tType]:(X0)).
% 0.22/0.36 thf(func_def_50, type, db1: !>[X0: $tType]:(X0)).
% 0.22/0.36 thf(func_def_51, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.36 thf(func_def_52, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.36 thf(func_def_53, type, db3: !>[X0: $tType]:(X0)).
% 0.22/0.36 thf(func_def_54, type, sP0: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X1 @ monoid_ext @ X1 @ X0 > $o))).
% 0.22/0.36 thf(func_def_55, type, sP1: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X1 @ monoid_ext @ X1 @ X0 > $o))).
% 0.22/0.36 thf(func_def_56, type, sP2: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X1 @ monoid_ext @ X1 @ X0 > $o))).
% 0.22/0.36 thf(func_def_57, type, sK3: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X1 @ monoid_ext @ X1 @ X0 > X1 > X1))).
% 0.22/0.36 thf(func_def_58, type, sK4: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ X2 > $o) > X2))).
% 0.22/0.36 thf(func_def_59, type, sK5: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ X2 > $o) > X0))).
% 0.22/0.36 thf(func_def_60, type, sK6: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ X2 > $o) > X1))).
% 0.22/0.36 thf(func_def_61, type, sK7: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X1 @ monoid_ext @ X1 @ X0 > X1))).
% 0.22/0.36 thf(func_def_62, type, sK8: !>[X0: $tType]:((set @ X0 > X0))).
% 0.22/0.36 thf(func_def_63, type, sK9: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 0.22/0.36 thf(func_def_64, type, sK10: !>[X0: $tType, X1: $tType]:((X0 > partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ X1 > X0))).
% 0.22/0.36 thf(func_def_65, type, sK11: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 0.22/0.36 thf(func_def_66, type, sK12: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 0.22/0.36 thf(func_def_67, type, sK13: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X1 @ X5 > X4))).
% 0.22/0.36 thf(func_def_68, type, sK14: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X1 @ X5 > X1))).
% 0.22/0.36 thf(func_def_69, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X1 @ X5 > X2))).
% 0.22/0.36 thf(func_def_70, type, sK16: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X1 @ X5 > X0))).
% 0.22/0.36 thf(func_def_71, type, sK17: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X1 @ X5 > X3))).
% 0.22/0.36 thf(func_def_72, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X1 @ X5 > X5))).
% 0.22/0.36 thf(func_def_73, type, sK19: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.22/0.36 thf(func_def_74, type, sK20: (a > a)).
% 0.22/0.36 thf(func_def_75, type, sK21: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X6 @ X1 > $o) > X3))).
% 0.22/0.36 thf(func_def_76, type, sK22: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X6 @ X1 > $o) > X5))).
% 0.22/0.36 thf(func_def_77, type, sK23: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X6 @ X1 > $o) > X2))).
% 0.22/0.36 thf(func_def_78, type, sK24: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X6 @ X1 > $o) > X4))).
% 0.22/0.36 thf(func_def_79, type, sK25: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X6 @ X1 > $o) > X0))).
% 0.22/0.36 thf(func_def_80, type, sK26: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X6 @ X1 > $o) > X6))).
% 0.22/0.36 thf(func_def_81, type, sK27: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X6 @ X1 > $o) > X1))).
% 0.22/0.36 thf(func_def_82, type, sK28: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X1 @ monoid_ext @ X1 @ X0 > X1))).
% 0.22/0.36 thf(func_def_83, type, sK29: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X1 @ monoid_ext @ X1 @ X0 > X1))).
% 0.22/0.36 thf(func_def_84, type, sK30: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X1 @ monoid_ext @ X1 @ X0 > X1))).
% 0.22/0.36 thf(func_def_85, type, sK31: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ X1 > X0))).
% 0.22/0.36 thf(func_def_86, type, sK32: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ X1 > X0))).
% 0.22/0.36 thf(func_def_87, type, sK33: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ X1 > X0))).
% 0.22/0.36 thf(func_def_88, type, sK34: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ X1 > X0))).
% 0.22/0.36 thf(func_def_89, type, sK35: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0))).
% 0.22/0.36 thf(func_def_90, type, sK36: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X1))).
% 0.22/0.36 thf(func_def_91, type, sK37: a).
% 0.22/0.36 thf(func_def_92, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X4 @ X0 > X2))).
% 0.22/0.36 thf(func_def_93, type, sK39: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X4 @ X0 > X4))).
% 0.22/0.36 thf(func_def_94, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X4 @ X0 > X3))).
% 0.22/0.36 thf(func_def_95, type, sK41: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X4 @ X0 > X0))).
% 0.22/0.36 thf(func_def_96, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X4 @ X0 > X1))).
% 0.22/0.36 thf(func_def_97, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ X2 > $o) > X0))).
% 0.22/0.36 thf(func_def_98, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ X2 > $o) > X1))).
% 0.22/0.36 thf(func_def_99, type, sK45: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ X2 > $o) > X3))).
% 0.22/0.36 thf(func_def_100, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ X2 > $o) > X2))).
% 0.22/0.36 thf(func_def_101, type, sK47: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.22/0.36 thf(func_def_102, type, sK48: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.22/0.36 thf(func_def_103, type, sK49: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.36 thf(func_def_104, type, sK50: a).
% 0.22/0.36 thf(func_def_105, type, sK51: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ X2 > X2))).
% 0.22/0.36 thf(func_def_106, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ X2 > X1))).
% 0.22/0.36 thf(func_def_107, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ X2 > X0))).
% 0.22/0.36 thf(func_def_108, type, sK54: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ X2 > X3))).
% 0.22/0.36 thf(func_def_109, type, sK55: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X3 @ X1 > $o) > X3))).
% 0.22/0.36 thf(func_def_110, type, sK56: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X3 @ X1 > $o) > X2))).
% 0.22/0.36 thf(func_def_111, type, sK57: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X3 @ X1 > $o) > X1))).
% 0.22/0.36 thf(func_def_112, type, sK58: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X3 @ X1 > $o) > X5))).
% 0.22/0.36 thf(func_def_113, type, sK59: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X3 @ X1 > $o) > X0))).
% 0.22/0.36 thf(func_def_114, type, sK60: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X3 @ X1 > $o) > X4))).
% 0.22/0.36 thf(func_def_115, type, sK61: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X1 @ monoid_ext @ X1 @ X0 > X1))).
% 0.22/0.36 thf(func_def_116, type, sK62: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X1 @ monoid_ext @ X1 @ X0 > X1))).
% 0.22/0.36 thf(func_def_117, type, sK63: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X1 @ monoid_ext @ X1 @ X0 > X1))).
% 0.22/0.36 thf(func_def_118, type, sK64: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X1 @ monoid_ext @ X1 @ X0 > X1))).
% 0.22/0.36 thf(func_def_119, type, sK65: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X1 @ monoid_ext @ X1 @ X0 > X1))).
% 0.22/0.36 thf(func_def_120, type, sK66: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X1 @ monoid_ext @ X1 @ X0 > X1))).
% 0.22/0.36 thf(func_def_121, type, sK67: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X1 @ monoid_ext @ X1 @ X0 > X1))).
% 0.22/0.36 thf(func_def_122, type, sK68: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X0 @ X3 > X3))).
% 0.22/0.36 thf(func_def_123, type, sK69: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X0 @ X3 > X0))).
% 0.22/0.36 thf(func_def_124, type, sK70: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X0 @ X3 > X2))).
% 0.22/0.36 thf(func_def_125, type, sK71: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X0 @ X3 > X5))).
% 0.22/0.36 thf(func_def_126, type, sK72: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X0 @ X3 > X4))).
% 0.22/0.36 thf(func_def_127, type, sK73: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X0 @ X3 > X6))).
% 0.22/0.36 thf(func_def_128, type, sK74: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X0 @ X3 > X1))).
% 0.22/0.36 thf(func_def_129, type, sK75: !>[X0: $tType]:((set @ X0 > X0))).
% 0.22/0.36 thf(func_def_130, type, sK76: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X0 @ X1 > $o) > X0))).
% 0.22/0.36 thf(func_def_131, type, sK77: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X0 @ X1 > $o) > X3))).
% 0.22/0.36 thf(func_def_132, type, sK78: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X0 @ X1 > $o) > X2))).
% 0.22/0.36 thf(func_def_133, type, sK79: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X0 @ X1 > $o) > X1))).
% 0.22/0.36 thf(func_def_134, type, sK80: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X0 @ X1 > $o) > X4))).
% 0.22/0.36 thf(func_def_135, type, sK81: (a > a)).
% 0.22/0.36 thf(func_def_136, type, sK82: !>[X0: $tType]:((set @ X0 > X0 > set @ X0 > X0 > set @ X0))).
% 0.22/0.36 thf(func_def_137, type, sK83: !>[X0: $tType]:((set @ X0 > X0))).
% 0.22/0.36 thf(func_def_138, type, sK84: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X0 @ X1 > X0))).
% 0.22/0.36 thf(func_def_139, type, sK85: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X0 @ X1 > X1))).
% 0.22/0.36 thf(func_def_140, type, sK86: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X0 @ X1 > X2))).
% 0.22/0.36 thf(func_def_141, type, sK87: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.22/0.36 thf(func_def_142, type, sK88: (a > a)).
% 0.22/0.36 thf(func_def_143, type, sK89: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X1 @ monoid_ext @ X1 @ X0 > X1 > X1))).
% 0.22/0.36 thf(func_def_144, type, sK90: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 0.22/0.36 thf(func_def_145, type, sK91: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X1 @ monoid_ext @ X1 @ X0 > X1))).
% 0.22/0.36 thf(func_def_146, type, sK92: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X1 @ monoid_ext @ X1 @ X0 > X1))).
% 0.22/0.36 thf(func_def_147, type, sK93: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X1 @ monoid_ext @ X1 @ X0 > X1))).
% 0.22/0.36 thf(func_def_148, type, sK94: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X1 @ monoid_ext @ X1 @ X0 > X1))).
% 0.22/0.36 thf(func_def_149, type, sK95: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X1 @ monoid_ext @ X1 @ X0 > X1))).
% 0.22/0.36 thf(func_def_150, type, sK96: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X1 @ monoid_ext @ X1 @ X0 > X1))).
% 0.22/0.36 thf(func_def_151, type, sK97: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X1 @ monoid_ext @ X1 @ X0 > X1))).
% 0.22/0.36 thf(func_def_152, type, sK98: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.22/0.36 thf(func_def_153, type, sK99: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.36 thf(func_def_154, type, sK100: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.36 thf(func_def_155, type, sK101: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X0))).
% 0.22/0.36 thf(func_def_156, type, sK102: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X1))).
% 0.22/0.36 thf(func_def_157, type, sK103: a).
% 0.22/0.36 thf(func_def_158, type, sK104: !>[X0: $tType, X1: $tType]:((X0 > partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ X1 > X0))).
% 0.22/0.36 thf(func_def_159, type, sK105: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.22/0.36 thf(func_def_160, type, sK106: !>[X0: $tType, X1: $tType]:((X0 > partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ X1 > X0))).
% 0.22/0.36 thf(func_def_161, type, vNOT: ($o > $o)).
% 0.22/0.36 thf(f1,axiom,(
% 0.22/0.36 (((mult @ a @ ring_ext @ a @ b @ r @ r2 @ r3)) = ((mult @ a @ ring_ext @ a @ b @ r @ r3 @ r2)))),
% 0.22/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_f3)).
% 0.22/0.36 thf(f2,axiom,(
% 0.22/0.36 (((mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3)) = ((mult @ a @ ring_ext @ a @ b @ r @ s3 @ s2)))),
% 0.22/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_f4)).
% 0.22/0.36 thf(f4,axiom,(
% 0.22/0.36 (((mult @ set @ product_prod @ a @ a @ product_unit @ (locali1768110497f_frac @ a @ b @ r @ s) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r2 @ s2) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r3 @ s3))) = ((locali1641774487f_frac @ a @ a @ product_unit @ rel @ (mult @ a @ ring_ext @ a @ b @ r @ r2 @ r3) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3))))),
% 0.22/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_f1)).
% 0.22/0.36 thf(f5,axiom,(
% 0.22/0.36 (((mult @ set @ product_prod @ a @ a @ product_unit @ (locali1768110497f_frac @ a @ b @ r @ s) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r3 @ s3) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r2 @ s2))) = ((locali1641774487f_frac @ a @ a @ product_unit @ rel @ (mult @ a @ ring_ext @ a @ b @ r @ r3 @ r2) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ s2))))),
% 0.22/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_f2)).
% 0.22/0.36 thf(f257,conjecture,(
% 0.22/0.36 (((mult @ set @ product_prod @ a @ a @ product_unit @ (locali1768110497f_frac @ a @ b @ r @ s) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r2 @ s2) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r3 @ s3))) = ((mult @ set @ product_prod @ a @ a @ product_unit @ (locali1768110497f_frac @ a @ b @ r @ s) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r3 @ s3) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r2 @ s2))))),
% 0.22/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.22/0.36 thf(f258,negated_conjecture,(
% 0.22/0.36 ~ (((mult @ set @ product_prod @ a @ a @ product_unit @ (locali1768110497f_frac @ a @ b @ r @ s) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r2 @ s2) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r3 @ s3))) = ((mult @ set @ product_prod @ a @ a @ product_unit @ (locali1768110497f_frac @ a @ b @ r @ s) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r3 @ s3) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r2 @ s2))))),
% 0.22/0.36 inference(negated_conjecture,[status(cth)],[f257])).
% 0.22/0.36 thf(f691,plain,(
% 0.22/0.36 (((mult @ set @ product_prod @ a @ a @ product_unit @ (locali1768110497f_frac @ a @ b @ r @ s) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r2 @ s2) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r3 @ s3))) != ((mult @ set @ product_prod @ a @ a @ product_unit @ (locali1768110497f_frac @ a @ b @ r @ s) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r3 @ s3) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r2 @ s2))))),
% 0.22/0.36 inference(flattening,[],[f258])).
% 0.22/0.36 thf(f1250,plain,(
% 0.22/0.36 (((mult @ set @ product_prod @ a @ a @ product_unit @ (locali1768110497f_frac @ a @ b @ r @ s) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r3 @ s3) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r2 @ s2))) = ((locali1641774487f_frac @ a @ a @ product_unit @ rel @ (mult @ a @ ring_ext @ a @ b @ r @ r3 @ r2) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ s2))))),
% 0.22/0.36 inference(cnf_transformation,[],[f5])).
% 0.22/0.36 thf(f1392,plain,(
% 0.22/0.36 (((mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3)) = ((mult @ a @ ring_ext @ a @ b @ r @ s3 @ s2)))),
% 0.22/0.36 inference(cnf_transformation,[],[f2])).
% 0.22/0.36 thf(f1403,plain,(
% 0.22/0.36 (((mult @ a @ ring_ext @ a @ b @ r @ r2 @ r3)) = ((mult @ a @ ring_ext @ a @ b @ r @ r3 @ r2)))),
% 0.22/0.36 inference(cnf_transformation,[],[f1])).
% 0.22/0.36 thf(f1464,plain,(
% 0.22/0.36 (((mult @ set @ product_prod @ a @ a @ product_unit @ (locali1768110497f_frac @ a @ b @ r @ s) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r2 @ s2) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r3 @ s3))) = ((locali1641774487f_frac @ a @ a @ product_unit @ rel @ (mult @ a @ ring_ext @ a @ b @ r @ r2 @ r3) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3))))),
% 0.22/0.36 inference(cnf_transformation,[],[f4])).
% 0.22/0.36 thf(f1510,plain,(
% 0.22/0.36 (((mult @ set @ product_prod @ a @ a @ product_unit @ (locali1768110497f_frac @ a @ b @ r @ s) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r2 @ s2) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r3 @ s3))) != ((mult @ set @ product_prod @ a @ a @ product_unit @ (locali1768110497f_frac @ a @ b @ r @ s) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r3 @ s3) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r2 @ s2))))),
% 0.22/0.36 inference(cnf_transformation,[],[f691])).
% 0.22/0.36 thf(f1692,definition,(
% 0.22/0.36 spl107_5 <=> (((mult @ a @ ring_ext @ a @ b @ r @ r2 @ r3)) = ((mult @ a @ ring_ext @ a @ b @ r @ r3 @ r2)))),
% 0.22/0.36 introduced(definition,[new_symbols(definition,[spl107_5])],[avatar_definition])).
% 0.22/0.36 thf(f1695,plain,(
% 0.22/0.36 spl107_5),
% 0.22/0.36 inference(avatar_split_clause,[],[f1403,f1692])).
% 0.22/0.36 thf(f1729,definition,(
% 0.22/0.36 spl107_13 <=> (((mult @ set @ product_prod @ a @ a @ product_unit @ (locali1768110497f_frac @ a @ b @ r @ s) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r2 @ s2) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r3 @ s3))) = ((locali1641774487f_frac @ a @ a @ product_unit @ rel @ (mult @ a @ ring_ext @ a @ b @ r @ r2 @ r3) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3))))),
% 0.22/0.36 introduced(definition,[new_symbols(definition,[spl107_13])],[avatar_definition])).
% 0.22/0.36 thf(f1732,plain,(
% 0.22/0.36 spl107_13),
% 0.22/0.36 inference(avatar_split_clause,[],[f1464,f1729])).
% 0.22/0.36 thf(f1750,definition,(
% 0.22/0.36 spl107_17 <=> (((mult @ set @ product_prod @ a @ a @ product_unit @ (locali1768110497f_frac @ a @ b @ r @ s) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r3 @ s3) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r2 @ s2))) = ((locali1641774487f_frac @ a @ a @ product_unit @ rel @ (mult @ a @ ring_ext @ a @ b @ r @ r3 @ r2) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ s2))))),
% 0.22/0.36 introduced(definition,[new_symbols(definition,[spl107_17])],[avatar_definition])).
% 0.22/0.36 thf(f1753,plain,(
% 0.22/0.36 spl107_17),
% 0.22/0.36 inference(avatar_split_clause,[],[f1250,f1750])).
% 0.22/0.36 thf(f1770,definition,(
% 0.22/0.36 spl107_21 <=> (((mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3)) = ((mult @ a @ ring_ext @ a @ b @ r @ s3 @ s2)))),
% 0.22/0.36 introduced(definition,[new_symbols(definition,[spl107_21])],[avatar_definition])).
% 0.22/0.36 thf(f1773,plain,(
% 0.22/0.36 spl107_21),
% 0.22/0.36 inference(avatar_split_clause,[],[f1392,f1770])).
% 0.22/0.36 thf(f1845,definition,(
% 0.22/0.36 spl107_36 <=> (((mult @ set @ product_prod @ a @ a @ product_unit @ (locali1768110497f_frac @ a @ b @ r @ s) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r2 @ s2) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r3 @ s3))) = ((mult @ set @ product_prod @ a @ a @ product_unit @ (locali1768110497f_frac @ a @ b @ r @ s) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r3 @ s3) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r2 @ s2))))),
% 0.22/0.36 introduced(definition,[new_symbols(definition,[spl107_36])],[avatar_definition])).
% 0.22/0.36 thf(f1848,plain,(
% 0.22/0.36 ~spl107_36),
% 0.22/0.36 inference(avatar_split_clause,[],[f1510,f1845])).
% 0.22/0.36 thf(f1860,definition,(
% 0.22/0.36 (((mult @ a @ ring_ext @ a @ b @ r @ r2 @ r3)) != ((mult @ a @ ring_ext @ a @ b @ r @ r3 @ r2))) | (((mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3)) != ((mult @ a @ ring_ext @ a @ b @ r @ s3 @ s2))) | (((mult @ set @ product_prod @ a @ a @ product_unit @ (locali1768110497f_frac @ a @ b @ r @ s) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r3 @ s3) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r2 @ s2))) != ((locali1641774487f_frac @ a @ a @ product_unit @ rel @ (mult @ a @ ring_ext @ a @ b @ r @ r3 @ r2) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ s2)))) | (((mult @ set @ product_prod @ a @ a @ product_unit @ (locali1768110497f_frac @ a @ b @ r @ s) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r2 @ s2) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r3 @ s3))) != ((locali1641774487f_frac @ a @ a @ product_unit @ rel @ (mult @ a @ ring_ext @ a @ b @ r @ r2 @ r3) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3)))) | (((mult @ set @ product_prod @ a @ a @ product_unit @ (locali1768110497f_frac @ a @ b @ r @ s) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r2 @ s2) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r3 @ s3))) = ((mult @ set @ product_prod @ a @ a @ product_unit @ (locali1768110497f_frac @ a @ b @ r @ s) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r3 @ s3) @ (locali1641774487f_frac @ a @ a @ product_unit @ rel @ r2 @ s2))))),
% 0.22/0.36 introduced(theory,[theory_tautology_sat_conflict])).
% 0.22/0.36 cnf(s4, plain, spl107_5, inference(sat_conversion,[],[f1695])).
% 0.22/0.36 cnf(s10, plain, spl107_13, inference(sat_conversion,[],[f1732])).
% 0.22/0.36 cnf(s15, plain, spl107_17, inference(sat_conversion,[],[f1753])).
% 0.22/0.36 cnf(s20, plain, spl107_21, inference(sat_conversion,[],[f1773])).
% 0.22/0.36 cnf(s36, plain, ~spl107_36, inference(sat_conversion,[],[f1848])).
% 0.22/0.36 cnf(s40, plain, ~spl107_5 | ~spl107_13 | ~spl107_17 | ~spl107_21 | spl107_36, inference(sat_conversion,[],[f1860])).
% 0.22/0.36 cnf(s41, plain, ~spl107_5, inference(rat,[],[s40,s36,s20,s15,s10])).
% 0.22/0.36 cnf(s42, plain, $false, inference(rat,[],[s4,s41])).
% 0.22/0.36 thf(f1861,plain,(
% 0.22/0.36 $false),
% 0.22/0.36 inference(avatar_sat_refutation,[],[s42])).
% 0.22/0.36 % SZS output end Proof for theBenchmark
% 0.22/0.36 % (1769076)------------------------------
% 0.22/0.36 % (1769076)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (1769076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (1769076)CaDiCaL version: 2.1.3
% 0.22/0.36 % (1769076)Termination reason: Refutation
% 0.22/0.36 % (1769076)Time elapsed: 0.043 s
% 0.22/0.36 % (1769076)Peak memory usage: 14 MB
% 0.22/0.36 % (1769076)Instructions burned: 175 (million)
% 0.22/0.36 % (1769068)Success in time 0.095 s
% 0.22/0.36 % Vampire exiting
%------------------------------------------------------------------------------