%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP027^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 08:10:25 AM UTC 2026
% Result : Theorem 0.21s 0.36s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP027^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n002.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 19:41:08 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.36 % (1750624)Will run a generic schedule for satisfiability detection.
% 0.21/0.36 % (1750631)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2809050361:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.36 % (1750630)% WARNING: option uhcvi not known.
% 0.21/0.36 % (1750632)dis+10_1_sil=32000:sp=arity:random_seed=3053858804:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.36 % (1750629)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3021467864_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.36 % (1750634)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1883171091:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.36 % (1750630)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1499841106:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.36 % (1750633)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2292183713:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.36 % (1750635)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1056776283:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.36 % (1750633)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.36 % (1750630)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.36 % (1750632)Instruction limit reached!
% 0.21/0.36 % (1750632)------------------------------
% 0.21/0.36 % (1750632)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (1750632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (1750632)CaDiCaL version: 2.1.3
% 0.21/0.36 % (1750632)Termination reason: Instruction limit
% 0.21/0.36 % (1750632)Termination phase: Property scanning
% 0.21/0.36 % (1750632)Time elapsed: 0.044 s
% 0.21/0.36 % (1750632)Peak memory usage: 11 MB
% 0.21/0.36 % (1750632)Instructions burned: 105 (million)
% 0.21/0.36 % (1750633)Instruction limit reached!
% 0.21/0.36 % (1750633)------------------------------
% 0.21/0.36 % (1750633)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (1750633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (1750633)CaDiCaL version: 2.1.3
% 0.21/0.36 % (1750633)Termination reason: Instruction limit
% 0.21/0.36 % (1750633)Termination phase: Property scanning
% 0.21/0.36 % (1750633)Time elapsed: 0.049 s
% 0.21/0.36 % (1750633)Peak memory usage: 11 MB
% 0.21/0.36 % (1750633)Instructions burned: 117 (million)
% 0.21/0.36 % (1750631) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1750624-1750631"...
% 0.21/0.36 % (1750634)Instruction limit reached!
% 0.21/0.36 % (1750634)------------------------------
% 0.21/0.36 % (1750634)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (1750634)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (1750634)CaDiCaL version: 2.1.3
% 0.21/0.36 % (1750634)Termination reason: Instruction limit
% 0.21/0.36 % (1750634)Termination phase: Function definition elimination
% 0.21/0.36 % (1750634)Time elapsed: 0.055 s
% 0.21/0.36 % (1750634)Peak memory usage: 11 MB
% 0.21/0.36 % (1750634)Instructions burned: 132 (million)
% 0.21/0.36 % (1750631)...printing done.
% 0.21/0.36 % (1750631)Refutation found. Thanks to Tanya!
% 0.21/0.36 % SZS status Theorem for theBenchmark
% 0.21/0.36 % SZS output start Proof for theBenchmark
% 0.21/0.36 thf(type_def_5, type, carrier_ext: ($tType * $tType) > $tType).
% 0.21/0.36 thf(type_def_6, type, module_ext: ($tType * $tType * $tType) > $tType).
% 0.21/0.36 thf(type_def_7, type, aGroup_ext: ($tType * $tType) > $tType).
% 0.21/0.36 thf(type_def_8, type, ring_ext: ($tType * $tType) > $tType).
% 0.21/0.36 thf(type_def_9, type, product_unit: $tType).
% 0.21/0.36 thf(type_def_10, type, set: $tType > $tType).
% 0.21/0.36 thf(type_def_11, type, nat: $tType).
% 0.21/0.36 thf(type_def_12, type, e: $tType).
% 0.21/0.36 thf(type_def_13, type, d: $tType).
% 0.21/0.36 thf(type_def_14, type, c: $tType).
% 0.21/0.36 thf(type_def_15, type, b: $tType).
% 0.21/0.36 thf(type_def_16, type, a: $tType).
% 0.21/0.36 thf(type_def_17, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.36 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 0.21/0.36 thf(func_def_1, type, plus: !>[X0: $tType]:($o)).
% 0.21/0.36 thf(func_def_2, type, ord: !>[X0: $tType]:($o)).
% 0.21/0.36 thf(func_def_3, type, group_add: !>[X0: $tType]:($o)).
% 0.21/0.36 thf(func_def_4, type, semigroup_add: !>[X0: $tType]:($o)).
% 0.21/0.36 thf(func_def_5, type, comm_monoid_add: !>[X0: $tType]:($o)).
% 0.21/0.36 thf(func_def_6, type, ab_semigroup_add: !>[X0: $tType]:($o)).
% 0.21/0.36 thf(func_def_7, type, cancel_semigroup_add: !>[X0: $tType]:($o)).
% 0.21/0.36 thf(func_def_8, type, ordere779506340up_add: !>[X0: $tType]:($o)).
% 0.21/0.36 thf(func_def_9, type, ordere236663937imp_le: !>[X0: $tType]:($o)).
% 0.21/0.36 thf(func_def_10, type, carrier: !>[X0: $tType, X1: $tType]:((carrier_ext @ X0 @ X1 > set @ X0))).
% 0.21/0.36 thf(func_def_11, type, j_rad: !>[X0: $tType, X1: $tType]:((carrier_ext @ X0 @ aGroup_ext @ X0 @ ring_ext @ X0 @ X1 > set @ X0))).
% 0.21/0.36 thf(func_def_12, type, ring: !>[X0: $tType, X1: $tType]:((carrier_ext @ X0 @ aGroup_ext @ X0 @ ring_ext @ X0 @ X1 > $o))).
% 0.21/0.36 thf(func_def_13, type, tp: !>[X0: $tType, X1: $tType]:((carrier_ext @ X0 @ aGroup_ext @ X0 @ ring_ext @ X0 @ X1 > X0 > X0 > X0))).
% 0.21/0.36 thf(func_def_14, type, un: !>[X0: $tType, X1: $tType]:((carrier_ext @ X0 @ aGroup_ext @ X0 @ ring_ext @ X0 @ X1 > X0))).
% 0.21/0.36 thf(func_def_15, type, sr: !>[X0: $tType, X1: $tType]:((carrier_ext @ X0 @ aGroup_ext @ X0 @ ring_ext @ X0 @ X1 > set @ X0 > carrier_ext @ X0 @ aGroup_ext @ X0 @ ring_ext @ X0 @ X1))).
% 0.21/0.36 thf(func_def_16, type, subring: !>[X0: $tType, X1: $tType, X2: $tType]:((carrier_ext @ X0 @ aGroup_ext @ X0 @ ring_ext @ X0 @ X1 > carrier_ext @ X0 @ aGroup_ext @ X0 @ ring_ext @ X0 @ X2 > $o))).
% 0.21/0.36 thf(func_def_17, type, unit: !>[X0: $tType, X1: $tType]:((carrier_ext @ X0 @ aGroup_ext @ X0 @ ring_ext @ X0 @ X1 > X0 > $o))).
% 0.21/0.36 thf(func_def_18, type, aGroup: !>[X0: $tType, X1: $tType]:((carrier_ext @ X0 @ aGroup_ext @ X0 @ X1 > $o))).
% 0.21/0.36 thf(func_def_19, type, mop: !>[X0: $tType, X1: $tType]:((carrier_ext @ X0 @ aGroup_ext @ X0 @ X1 > X0 > X0))).
% 0.21/0.36 thf(func_def_20, type, pop: !>[X0: $tType, X1: $tType]:((carrier_ext @ X0 @ aGroup_ext @ X0 @ X1 > X0 > X0 > X0))).
% 0.21/0.36 thf(func_def_21, type, aset_sum: !>[X0: $tType, X1: $tType]:((carrier_ext @ X0 @ aGroup_ext @ X0 @ X1 > set @ X0 > set @ X0 > set @ X0))).
% 0.21/0.36 thf(func_def_22, type, carr_dsumag: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ X0 > (X0 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X2) > set @ (X0 > X1)))).
% 0.21/0.36 thf(func_def_23, type, carr_prodag: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ X0 > (X0 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X2) > set @ (X0 > X1)))).
% 0.21/0.36 thf(func_def_24, type, local_ring: !>[X0: $tType, X1: $tType]:((carrier_ext @ X0 @ aGroup_ext @ X0 @ ring_ext @ X0 @ X1 > $o))).
% 0.21/0.36 thf(func_def_25, type, maximal_ideal: !>[X0: $tType, X1: $tType]:((carrier_ext @ X0 @ aGroup_ext @ X0 @ ring_ext @ X0 @ X1 > set @ X0 > $o))).
% 0.21/0.36 thf(func_def_26, type, mul_closed_set: !>[X0: $tType, X1: $tType]:((carrier_ext @ X0 @ aGroup_ext @ X0 @ ring_ext @ X0 @ X1 > set @ X0 > $o))).
% 0.21/0.36 thf(func_def_27, type, nscal: !>[X0: $tType, X1: $tType]:((carrier_ext @ X0 @ aGroup_ext @ X0 @ ring_ext @ X0 @ X1 > X0 > nat > X0))).
% 0.21/0.36 thf(func_def_28, type, primary_ideal: !>[X0: $tType, X1: $tType]:((carrier_ext @ X0 @ aGroup_ext @ X0 @ ring_ext @ X0 @ X1 > set @ X0 > $o))).
% 0.21/0.36 thf(func_def_29, type, prod_mOp: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ X0 > (X0 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X2) > (X0 > X1) > X0 > X1))).
% 0.21/0.36 thf(func_def_30, type, prod_pOp: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ X0 > (X0 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X2) > (X0 > X1) > (X0 > X1) > X0 > X1))).
% 0.21/0.36 thf(func_def_31, type, prod_zero: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ X0 > (X0 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X2) > X0 > X1))).
% 0.21/0.36 thf(func_def_32, type, rInvim: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((carrier_ext @ X0 @ aGroup_ext @ X0 @ ring_ext @ X0 @ X1 > carrier_ext @ X2 @ aGroup_ext @ X2 @ ring_ext @ X2 @ X3 > (X0 > X2) > set @ X2 > set @ X0))).
% 0.21/0.36 thf(func_def_33, type, sr2: !>[X0: $tType, X1: $tType]:((carrier_ext @ X0 @ aGroup_ext @ X0 @ ring_ext @ X0 @ X1 > set @ X0 > $o))).
% 0.21/0.36 thf(func_def_34, type, zeroring: !>[X0: $tType, X1: $tType]:((carrier_ext @ X0 @ aGroup_ext @ X0 @ ring_ext @ X0 @ X1 > $o))).
% 0.21/0.36 thf(func_def_35, type, sum_mult: !>[X0: $tType, X1: $tType]:((carrier_ext @ X0 @ aGroup_ext @ X0 @ ring_ext @ X0 @ X1 > set @ X0 > set @ X0 > set @ X0))).
% 0.21/0.36 thf(func_def_36, type, module: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((carrier_ext @ X0 @ aGroup_ext @ X0 @ module_ext @ X0 @ X1 @ X2 > carrier_ext @ X1 @ aGroup_ext @ X1 @ ring_ext @ X1 @ X3 > $o))).
% 0.21/0.36 thf(func_def_37, type, sprod: !>[X0: $tType, X1: $tType, X2: $tType]:((carrier_ext @ X0 @ aGroup_ext @ X0 @ module_ext @ X0 @ X1 @ X2 > X1 > X0 > X0))).
% 0.21/0.36 thf(func_def_38, type, mHom: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((carrier_ext @ X0 @ aGroup_ext @ X0 @ ring_ext @ X0 @ X1 > carrier_ext @ X2 @ aGroup_ext @ X2 @ module_ext @ X2 @ X0 @ X3 > carrier_ext @ X4 @ aGroup_ext @ X4 @ module_ext @ X4 @ X0 @ X5 > set @ (X2 > X4)))).
% 0.21/0.36 thf(func_def_39, type, algebr1000837334_prodM: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((carrier_ext @ X0 @ aGroup_ext @ X0 @ ring_ext @ X0 @ X1 > set @ X2 > (X2 > carrier_ext @ X3 @ aGroup_ext @ X3 @ module_ext @ X3 @ X0 @ X4) > carrier_ext @ (X2 > X3) @ aGroup_ext @ (X2 > X3) @ module_ext @ (X2 > X3) @ X0 @ product_unit))).
% 0.21/0.36 thf(func_def_40, type, algebr142713364_sprod: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((carrier_ext @ X0 @ aGroup_ext @ X0 @ ring_ext @ X0 @ X1 > set @ X2 > (X2 > carrier_ext @ X3 @ aGroup_ext @ X3 @ module_ext @ X3 @ X0 @ X4) > X0 > (X2 > X3) > X2 > X3))).
% 0.21/0.36 thf(func_def_41, type, pi: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > set @ X1) > set @ (X0 > X1)))).
% 0.21/0.36 thf(func_def_42, type, plus_plus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.21/0.36 thf(func_def_43, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.36 thf(func_def_44, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.21/0.36 thf(func_def_45, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.21/0.36 thf(func_def_46, type, i: set @ c).
% 0.21/0.36 thf(func_def_47, type, m: (c > carrier_ext @ d @ aGroup_ext @ d @ module_ext @ d @ a @ e)).
% 0.21/0.36 thf(func_def_48, type, r: carrier_ext @ a @ aGroup_ext @ a @ ring_ext @ a @ b).
% 0.21/0.36 thf(func_def_52, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.36 thf(func_def_53, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.36 thf(func_def_54, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.21/0.36 thf(func_def_55, type, vIMP: ($o > $o > $o)).
% 0.21/0.36 thf(func_def_56, type, vAND: ($o > $o > $o)).
% 0.21/0.36 thf(func_def_57, type, db4: !>[X0: $tType]:(X0)).
% 0.21/0.36 thf(func_def_58, type, db2: !>[X0: $tType]:(X0)).
% 0.21/0.36 thf(func_def_59, type, db1: !>[X0: $tType]:(X0)).
% 0.21/0.36 thf(func_def_60, type, db3: !>[X0: $tType]:(X0)).
% 0.21/0.36 thf(func_def_61, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.36 thf(func_def_62, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.21/0.36 thf(func_def_63, type, sK0: !>[X0: $tType, X1: $tType]:(((X1 > set @ X0) > (X1 > X0) > set @ X1 > X1))).
% 0.21/0.36 thf(func_def_64, type, sK1: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > carrier_ext @ X1 @ aGroup_ext @ X1 @ module_ext @ X1 @ a @ X0) > set @ X2 > X2))).
% 0.21/0.36 thf(func_def_65, type, sK2: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > carrier_ext @ X1 @ aGroup_ext @ X1 @ module_ext @ X1 @ a @ X0) > set @ X2 > X2))).
% 0.21/0.36 thf(func_def_66, type, sK3: !>[X0: $tType, X1: $tType]:((set @ X0 > (X1 > X0) > set @ X1 > X1))).
% 0.21/0.36 thf(func_def_67, type, sK4: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X0) > set @ X2 > X2))).
% 0.21/0.36 thf(func_def_68, type, sK5: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 0.21/0.36 thf(func_def_69, type, sK6: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > carrier_ext @ X1 @ aGroup_ext @ X1 @ module_ext @ X1 @ a @ X0) > set @ X2 > X2))).
% 0.21/0.36 thf(func_def_70, type, sK7: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 0.21/0.36 thf(func_def_71, type, sK8: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((X4 > carrier_ext @ X3 @ aGroup_ext @ X3 @ module_ext @ X3 @ X0 @ X1) > set @ X4 > carrier_ext @ X0 @ aGroup_ext @ X0 @ ring_ext @ X0 @ X2 > X4))).
% 0.21/0.36 thf(func_def_72, type, sK9: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 0.21/0.36 thf(func_def_73, type, sK10: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X0) > set @ X2 > X2))).
% 0.21/0.36 thf(func_def_74, type, sK11: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X0) > (X2 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X0) > set @ X2 > X2))).
% 0.21/0.36 thf(func_def_75, type, sK12: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X0) > set @ X2 > X2))).
% 0.21/0.36 thf(func_def_76, type, sK13: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X0) > (X2 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X0) > set @ X2 > X2))).
% 0.21/0.36 thf(func_def_77, type, sK14: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X0) > set @ X2 > X2))).
% 0.21/0.36 thf(func_def_78, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X0) > (X2 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X0) > set @ X2 > X2))).
% 0.21/0.36 thf(func_def_79, type, sK16: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X0) > set @ X2 > X2))).
% 0.21/0.36 thf(func_def_80, type, sK17: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X0) > (X2 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X0) > set @ X2 > X2))).
% 0.21/0.36 thf(func_def_81, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X0) > set @ X2 > X2))).
% 0.21/0.36 thf(func_def_82, type, sK19: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((X4 > carrier_ext @ X3 @ aGroup_ext @ X3 @ module_ext @ X3 @ X2 @ X1) > set @ X4 > carrier_ext @ X2 @ aGroup_ext @ X2 @ ring_ext @ X2 @ X0 > X4))).
% 0.21/0.36 thf(func_def_83, type, sK20: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((X4 > carrier_ext @ X3 @ aGroup_ext @ X3 @ module_ext @ X3 @ X2 @ X1) > set @ X4 > carrier_ext @ X2 @ aGroup_ext @ X2 @ ring_ext @ X2 @ X0 > X4))).
% 0.21/0.36 thf(func_def_84, type, sK21: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X0) > set @ X2 > X2))).
% 0.21/0.36 thf(func_def_85, type, sK22: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X0) > set @ X2 > X2))).
% 0.21/0.36 thf(func_def_86, type, sK23: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X0) > set @ X2 > X2))).
% 0.21/0.36 thf(func_def_87, type, sK24: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X0) > set @ X2 > X2))).
% 0.21/0.36 thf(func_def_88, type, sK25: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X0) > set @ X2 > X2))).
% 0.21/0.36 thf(func_def_89, type, sK26: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X0) > set @ X2 > X2))).
% 0.21/0.36 thf(func_def_90, type, sK27: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 0.21/0.36 thf(func_def_91, type, sK28: !>[X0: $tType, X1: $tType]:(((X1 > set @ X0) > (X1 > X0) > set @ X1 > X1))).
% 0.21/0.36 thf(func_def_92, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > carrier_ext @ X1 @ aGroup_ext @ X1 @ module_ext @ X1 @ a @ X0) > set @ X2 > X2))).
% 0.21/0.36 thf(func_def_93, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X0) > set @ X2 > X2))).
% 0.21/0.36 thf(func_def_94, type, sK31: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.21/0.36 thf(func_def_95, type, sK32: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.21/0.36 thf(func_def_96, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X0) > set @ X2 > X2))).
% 0.21/0.36 thf(func_def_97, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X0) > set @ X2 > X2))).
% 0.21/0.36 thf(func_def_98, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X0) > set @ X2 > X2))).
% 0.21/0.36 thf(func_def_99, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X0) > set @ X2 > X2))).
% 0.21/0.36 thf(func_def_100, type, sK37: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((X4 > carrier_ext @ X3 @ aGroup_ext @ X3 @ module_ext @ X3 @ X1 @ X2) > set @ X4 > carrier_ext @ X1 @ aGroup_ext @ X1 @ ring_ext @ X1 @ X0 > X4))).
% 0.21/0.36 thf(func_def_101, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X0) > set @ X2 > X2))).
% 0.21/0.36 thf(func_def_102, type, sK39: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X3 > X2) > (X3 > X2) > carrier_ext @ X3 @ aGroup_ext @ X3 @ module_ext @ X3 @ X1 @ X0 > X3))).
% 0.21/0.36 thf(func_def_103, type, sK40: set @ a).
% 0.21/0.36 thf(func_def_104, type, sK41: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.21/0.36 thf(func_def_105, type, sK42: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.21/0.36 thf(func_def_106, type, sK43: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.21/0.36 thf(func_def_107, type, sK44: !>[X0: $tType, X1: $tType]:(((X1 > set @ X0) > (X1 > set @ X0) > set @ X1 > X1))).
% 0.21/0.36 thf(func_def_108, type, sK45: !>[X0: $tType, X1: $tType]:((carrier_ext @ X1 @ aGroup_ext @ X1 @ ring_ext @ X1 @ X0 > set @ X1))).
% 0.21/0.36 thf(func_def_109, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X0) > set @ X2 > X2))).
% 0.21/0.36 thf(func_def_110, type, sK47: (a > set @ a)).
% 0.21/0.36 thf(func_def_111, type, sK48: (nat > nat > nat)).
% 0.21/0.36 thf(func_def_112, type, sK49: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X0) > set @ X2 > X2))).
% 0.21/0.36 thf(func_def_113, type, sK50: !>[X0: $tType, X1: $tType]:((X1 > carrier_ext @ X1 @ aGroup_ext @ X1 @ ring_ext @ X1 @ X0 > set @ X1))).
% 0.21/0.36 thf(func_def_114, type, sK51: !>[X0: $tType, X1: $tType]:((X1 > set @ X1 > set @ X1 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X0 > X1))).
% 0.21/0.36 thf(func_def_115, type, sK52: !>[X0: $tType, X1: $tType]:((X1 > set @ X1 > set @ X1 > carrier_ext @ X1 @ aGroup_ext @ X1 @ X0 > X1))).
% 0.21/0.36 thf(func_def_116, type, sK53: (set @ a > a)).
% 0.21/0.36 thf(func_def_117, type, sK54: (c > d)).
% 0.21/0.36 thf(func_def_118, type, vNOT: ($o > $o)).
% 0.21/0.36 thf(func_def_119, type, sK55: !>[X0: $tType, X1: $tType]:((carrier_ext @ X1 @ aGroup_ext @ X1 @ ring_ext @ X1 @ X0 > set @ X1 > X1))).
% 0.21/0.36 thf(func_def_120, type, sK56: !>[X0: $tType, X1: $tType]:((set @ X1 > carrier_ext @ X1 @ aGroup_ext @ X1 @ ring_ext @ X1 @ X0 > X1))).
% 0.21/0.36 thf(func_def_121, type, sK57: (set @ a > a)).
% 0.21/0.36 thf(func_def_122, type, sK58: (set @ a > a)).
% 0.21/0.36 thf(func_def_123, type, sK59: (a > a > a)).
% 0.21/0.36 thf(func_def_124, type, sK60: !>[X0: $tType, X1: $tType]:((X1 > carrier_ext @ X1 @ aGroup_ext @ X1 @ ring_ext @ X1 @ X0 > X1))).
% 0.21/0.36 thf(func_def_125, type, sK61: !>[X0: $tType, X1: $tType]:((X1 > carrier_ext @ X1 @ aGroup_ext @ X1 @ ring_ext @ X1 @ X0 > X1))).
% 0.21/0.36 thf(func_def_126, type, sK62: (a > a)).
% 0.21/0.36 thf(func_def_127, type, sK63: (a > a)).
% 0.21/0.36 thf(func_def_128, type, sK64: !>[X0: $tType, X1: $tType]:((set @ X1 > carrier_ext @ X1 @ aGroup_ext @ X1 @ ring_ext @ X1 @ X0 > X1))).
% 0.21/0.36 thf(func_def_129, type, sK65: !>[X0: $tType, X1: $tType]:((set @ X1 > carrier_ext @ X1 @ aGroup_ext @ X1 @ ring_ext @ X1 @ X0 > X1))).
% 0.21/0.36 thf(func_def_130, type, sK66: !>[X0: $tType, X1: $tType]:((set @ X1 > carrier_ext @ X1 @ aGroup_ext @ X1 @ ring_ext @ X1 @ X0 > X1))).
% 0.21/0.36 thf(func_def_131, type, sK67: !>[X0: $tType, X1: $tType]:((set @ X1 > carrier_ext @ X1 @ aGroup_ext @ X1 @ ring_ext @ X1 @ X0 > X1))).
% 0.21/0.36 thf(func_def_132, type, sK68: (set @ a > a)).
% 0.21/0.36 thf(func_def_133, type, sK69: (set @ a > a)).
% 0.21/0.36 thf(func_def_134, type, sK70: (set @ a > a)).
% 0.21/0.36 thf(func_def_135, type, sK71: (set @ a > a)).
% 0.21/0.36 thf(func_def_136, type, sK72: !>[X0: $tType, X1: $tType]:((set @ X1 > carrier_ext @ X1 @ aGroup_ext @ X1 @ ring_ext @ X1 @ X0 > X1))).
% 0.21/0.36 thf(func_def_137, type, sK73: !>[X0: $tType, X1: $tType]:((set @ X1 > carrier_ext @ X1 @ aGroup_ext @ X1 @ ring_ext @ X1 @ X0 > X1))).
% 0.21/0.36 thf(func_def_138, type, sK74: !>[X0: $tType, X1: $tType]:((set @ X1 > carrier_ext @ X1 @ aGroup_ext @ X1 @ ring_ext @ X1 @ X0 > X1))).
% 0.21/0.36 thf(func_def_139, type, sK75: !>[X0: $tType, X1: $tType]:((set @ X1 > carrier_ext @ X1 @ aGroup_ext @ X1 @ ring_ext @ X1 @ X0 > X1))).
% 0.21/0.36 thf(func_def_140, type, sK76: !>[X0: $tType, X1: $tType]:((set @ X1 > carrier_ext @ X1 @ aGroup_ext @ X1 @ ring_ext @ X1 @ X0 > X1))).
% 0.21/0.36 thf(func_def_141, type, sK77: !>[X0: $tType, X1: $tType]:((set @ X1 > carrier_ext @ X1 @ aGroup_ext @ X1 @ ring_ext @ X1 @ X0 > X1))).
% 0.21/0.36 thf(func_def_142, type, sK78: !>[X0: $tType, X1: $tType]:((set @ X1 > carrier_ext @ X1 @ aGroup_ext @ X1 @ ring_ext @ X1 @ X0 > X1))).
% 0.21/0.36 thf(func_def_143, type, sK79: !>[X0: $tType, X1: $tType]:((set @ X1 > carrier_ext @ X1 @ aGroup_ext @ X1 @ ring_ext @ X1 @ X0 > X1))).
% 0.21/0.36 thf(func_def_144, type, sK80: (set @ a > a)).
% 0.21/0.36 thf(func_def_145, type, sK81: (set @ a > a)).
% 0.21/0.36 thf(func_def_146, type, sK82: (set @ a > a)).
% 0.21/0.36 thf(func_def_147, type, sK83: (set @ a > a)).
% 0.21/0.36 thf(func_def_148, type, sK84: (set @ a > a)).
% 0.21/0.36 thf(func_def_149, type, sK85: (set @ a > a)).
% 0.21/0.36 thf(func_def_150, type, sK86: (set @ a > a)).
% 0.21/0.36 thf(func_def_151, type, sK87: (set @ a > a)).
% 0.21/0.36 thf(func_def_152, type, sK88: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > set @ X0) > (X1 > X0) > X1))).
% 0.21/0.36 thf(func_def_153, type, sK89: c).
% 0.21/0.36 thf(f270,axiom,(
% 0.21/0.36 ! [X2 : (c > d)] : ((member @ (c > d) @ X2 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m)) => (((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ (prod_zero @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ X2)) = X2)) & (member @ (c > d) @ (prod_zero @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m)) & ! [X2 : (c > d)] : ((member @ (c > d) @ X2 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m)) => (((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ (prod_mOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X2) @ X2)) = ((prod_zero @ c @ d @ module_ext @ d @ a @ e @ i @ m)))) & (member @ ((c > d) > c > d) @ (prod_mOp @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ (pi @ (c > d) @ (c > d) @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ (^[X0 : (c > d)] : ((carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))))) & ! [X2 : (c > d)] : ((member @ (c > d) @ X2 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m)) => ! [X3 : (c > d)] : ((member @ (c > d) @ X3 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m)) => (((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X2 @ X3)) = ((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X3 @ X2))))) & ! [X2 : (c > d)] : ((member @ (c > d) @ X2 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m)) => ! [X3 : (c > d)] : ((member @ (c > d) @ X3 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m)) => ! [X4 : (c > d)] : ((member @ (c > d) @ X4 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m)) => (((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ (prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X2 @ X3) @ X4)) = ((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X2 @ (prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X3 @ X4))))))) & (member @ ((c > d) > (c > d) > c > d) @ (prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ (pi @ (c > d) @ ((c > d) > c > d) @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ (^[X0 : (c > d)] : ((pi @ (c > d) @ (c > d) @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ (^[X1 : (c > d)] : ((carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))))))))),
% 0.21/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)).
% 0.21/0.36 thf(f271,conjecture,(
% 0.21/0.36 ! [X0 : (c > d)] : ((((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X0 @ (prod_zero @ c @ d @ module_ext @ d @ a @ e @ i @ m))) = X0) | ~(member @ (c > d) @ X0 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m)))),
% 0.21/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2)).
% 0.21/0.36 thf(f272,negated_conjecture,(
% 0.21/0.36 ~ ! [X0 : (c > d)] : ((((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X0 @ (prod_zero @ c @ d @ module_ext @ d @ a @ e @ i @ m))) = X0) | ~(member @ (c > d) @ X0 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m)))),
% 0.21/0.36 inference(negated_conjecture,[status(cth)],[f271])).
% 0.21/0.36 thf(f803,plain,(
% 0.21/0.36 ! [X0 : (c > d)] : ((member @ (c > d) @ X0 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m)) => (((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ (prod_zero @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ X0)) = X0)) & (member @ (c > d) @ (prod_zero @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m)) & ! [X1 : (c > d)] : ((member @ (c > d) @ X1 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m)) => (((prod_zero @ c @ d @ module_ext @ d @ a @ e @ i @ m)) = ((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ (prod_mOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X1) @ X1)))) & (member @ ((c > d) > c > d) @ (prod_mOp @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ (pi @ (c > d) @ (c > d) @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ (^[X2 : (c > d)] : ((carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))))) & ! [X3 : (c > d)] : ((member @ (c > d) @ X3 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m)) => ! [X4 : (c > d)] : ((member @ (c > d) @ X4 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m)) => (((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X3 @ X4)) = ((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X4 @ X3))))) & ! [X5 : (c > d)] : ((member @ (c > d) @ X5 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m)) => ! [X6 : (c > d)] : ((member @ (c > d) @ X6 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m)) => ! [X7 : (c > d)] : ((member @ (c > d) @ X7 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m)) => (((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ (prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X5 @ X6) @ X7)) = ((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X5 @ (prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X6 @ X7))))))) & (member @ ((c > d) > (c > d) > c > d) @ (prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ (pi @ (c > d) @ ((c > d) > c > d) @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ (^[X8 : (c > d)] : ((pi @ (c > d) @ (c > d) @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ (^[X9 : (c > d)] : ((carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))))))))),
% 0.21/0.36 inference(rectify,[],[f270])).
% 0.21/0.36 thf(f804,plain,(
% 0.21/0.36 ! [X0 : (c > d)] : ((((member @ (c > d) @ X0 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))) = $true) => (((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ (prod_zero @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ X0)) = X0)) & (((member @ (c > d) @ (prod_zero @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))) = $true) & ! [X1 : (c > d)] : (($true = ((member @ (c > d) @ X1 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m)))) => (((prod_zero @ c @ d @ module_ext @ d @ a @ e @ i @ m)) = ((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ (prod_mOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X1) @ X1)))) & ($true = ((member @ ((c > d) > c > d) @ (prod_mOp @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ (pi @ (c > d) @ (c > d) @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ (^[Y0 : c > d]: (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m)))))) & ! [X3 : (c > d)] : ((((member @ (c > d) @ X3 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))) = $true) => ! [X4 : (c > d)] : ((((member @ (c > d) @ X4 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))) = $true) => (((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X3 @ X4)) = ((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X4 @ X3))))) & ! [X5 : (c > d)] : (($true = ((member @ (c > d) @ X5 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m)))) => ! [X6 : (c > d)] : (($true = ((member @ (c > d) @ X6 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m)))) => ! [X7 : (c > d)] : (($true = ((member @ (c > d) @ X7 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m)))) => (((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ (prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X5 @ X6) @ X7)) = ((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X5 @ (prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X6 @ X7))))))) & ($true = ((member @ ((c > d) > (c > d) > c > d) @ (prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ (pi @ (c > d) @ ((c > d) > c > d) @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ (^[Y0 : c > d]: (pi @ (c > d) @ (c > d) @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ (^[Y1 : c > d]: (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))))))))),
% 0.21/0.36 inference(fool_elimination,[],[f803])).
% 0.21/0.36 thf(f805,plain,(
% 0.21/0.36 ~ ! [X0 : (c > d)] : ((((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X0 @ (prod_zero @ c @ d @ module_ext @ d @ a @ e @ i @ m))) = X0) | ~(member @ (c > d) @ X0 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m)))),
% 0.21/0.36 inference(rectify,[],[f272])).
% 0.21/0.36 thf(f806,plain,(
% 0.21/0.36 ~ ! [X0 : (c > d)] : ((((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X0 @ (prod_zero @ c @ d @ module_ext @ d @ a @ e @ i @ m))) = X0) | ~ (((member @ (c > d) @ X0 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))) = $true))),
% 0.21/0.36 inference(fool_elimination,[],[f805])).
% 0.21/0.36 thf(f823,plain,(
% 0.21/0.36 ! [X0 : (c > d)] : ((((member @ (c > d) @ X0 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))) = $true) => (((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ (prod_zero @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ X0)) = X0)) & (((member @ (c > d) @ (prod_zero @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))) = $true) & ! [X1 : (c > d)] : (($true = ((member @ (c > d) @ X1 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m)))) => (((prod_zero @ c @ d @ module_ext @ d @ a @ e @ i @ m)) = ((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ (prod_mOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X1) @ X1)))) & ($true = ((member @ ((c > d) > c > d) @ (prod_mOp @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ (pi @ (c > d) @ (c > d) @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ (^[Y0 : c > d]: (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m)))))) & ! [X2 : (c > d)] : ((((member @ (c > d) @ X2 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))) = $true) => ! [X3 : (c > d)] : ((((member @ (c > d) @ X3 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))) = $true) => (((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X2 @ X3)) = ((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X3 @ X2))))) & ! [X4 : (c > d)] : ((((member @ (c > d) @ X4 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))) = $true) => ! [X5 : (c > d)] : (($true = ((member @ (c > d) @ X5 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m)))) => ! [X6 : (c > d)] : (($true = ((member @ (c > d) @ X6 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m)))) => (((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ (prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X4 @ X5) @ X6)) = ((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X4 @ (prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X5 @ X6))))))) & ($true = ((member @ ((c > d) > (c > d) > c > d) @ (prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ (pi @ (c > d) @ ((c > d) > c > d) @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ (^[Y0 : c > d]: (pi @ (c > d) @ (c > d) @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ (^[Y1 : c > d]: (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))))))))),
% 0.21/0.36 inference(rectify,[],[f804])).
% 0.21/0.36 thf(f824,plain,(
% 0.21/0.36 ~ ! [X0 : (c > d)] : ((((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X0 @ (prod_zero @ c @ d @ module_ext @ d @ a @ e @ i @ m))) = X0) | (((member @ (c > d) @ X0 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))) != $true))),
% 0.21/0.36 inference(flattening,[],[f806])).
% 0.21/0.36 thf(f1233,plain,(
% 0.21/0.36 ! [X0 : (c > d)] : ((((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ (prod_zero @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ X0)) = X0) | (((member @ (c > d) @ X0 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))) != $true)) & (((member @ (c > d) @ (prod_zero @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))) = $true) & ! [X1 : (c > d)] : ((((prod_zero @ c @ d @ module_ext @ d @ a @ e @ i @ m)) = ((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ (prod_mOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X1) @ X1))) | ($true != ((member @ (c > d) @ X1 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))))) & ($true = ((member @ ((c > d) > c > d) @ (prod_mOp @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ (pi @ (c > d) @ (c > d) @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ (^[Y0 : c > d]: (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m)))))) & ! [X2 : (c > d)] : (! [X3 : (c > d)] : ((((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X2 @ X3)) = ((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X3 @ X2))) | (((member @ (c > d) @ X3 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))) != $true)) | (((member @ (c > d) @ X2 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))) != $true)) & ! [X4 : (c > d)] : (! [X5 : (c > d)] : (! [X6 : (c > d)] : ((((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ (prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X4 @ X5) @ X6)) = ((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X4 @ (prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X5 @ X6)))) | ($true != ((member @ (c > d) @ X6 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))))) | ($true != ((member @ (c > d) @ X5 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))))) | (((member @ (c > d) @ X4 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))) != $true)) & ($true = ((member @ ((c > d) > (c > d) > c > d) @ (prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ (pi @ (c > d) @ ((c > d) > c > d) @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ (^[Y0 : c > d]: (pi @ (c > d) @ (c > d) @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ (^[Y1 : c > d]: (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))))))))),
% 0.21/0.36 inference(ennf_transformation,[],[f823])).
% 0.21/0.36 thf(f1234,plain,(
% 0.21/0.36 ? [X0 : (c > d)] : ((((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X0 @ (prod_zero @ c @ d @ module_ext @ d @ a @ e @ i @ m))) != X0) & (((member @ (c > d) @ X0 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))) = $true))),
% 0.21/0.36 inference(ennf_transformation,[],[f824])).
% 0.21/0.36 thf(f1288,plain,(
% 0.21/0.36 (sK54 != ((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ sK54 @ (prod_zero @ c @ d @ module_ext @ d @ a @ e @ i @ m)))) & ($true = ((member @ (c > d) @ sK54 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))))),
% 0.21/0.36 inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(X0,sK54)],[f1234])).
% 0.21/0.36 thf(f1620,plain,(
% 0.21/0.36 ( ! [X2 : (c > d),X3 : (c > d)] : ((((member @ (c > d) @ X3 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))) != $true) | (((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X2 @ X3)) = ((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X3 @ X2))) | (((member @ (c > d) @ X2 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))) != $true)) )),
% 0.21/0.36 inference(cnf_transformation,[],[f1233])).
% 0.21/0.36 thf(f1623,plain,(
% 0.21/0.36 (((member @ (c > d) @ (prod_zero @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))) = $true)),
% 0.21/0.36 inference(cnf_transformation,[],[f1233])).
% 0.21/0.36 thf(f1624,plain,(
% 0.21/0.36 ( ! [X0 : (c > d)] : ((((member @ (c > d) @ X0 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))) != $true) | (((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ (prod_zero @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ X0)) = X0)) )),
% 0.21/0.36 inference(cnf_transformation,[],[f1233])).
% 0.21/0.36 thf(f1625,plain,(
% 0.21/0.36 ($true = ((member @ (c > d) @ sK54 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))))),
% 0.21/0.36 inference(cnf_transformation,[],[f1288])).
% 0.21/0.36 thf(f1626,plain,(
% 0.21/0.36 (sK54 != ((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ sK54 @ (prod_zero @ c @ d @ module_ext @ d @ a @ e @ i @ m))))),
% 0.21/0.36 inference(cnf_transformation,[],[f1288])).
% 0.21/0.36 thf(f1969,plain,(
% 0.21/0.36 ($true != $true) | (sK54 = ((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ (prod_zero @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ sK54)))),
% 0.21/0.36 inference(constrained_superposition,[],[f1624,f1625])).
% 0.21/0.36 thf(f1972,plain,(
% 0.21/0.36 (sK54 = ((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ (prod_zero @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ sK54)))),
% 0.21/0.36 inference(trivial_inequality_removal,[],[f1969])).
% 0.21/0.36 thf(f2175,plain,(
% 0.21/0.36 ( ! [X0 : (c > d)] : (($true != $true) | (((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X0 @ sK54)) = ((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ sK54 @ X0))) | (((member @ (c > d) @ X0 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))) != $true)) )),
% 0.21/0.36 inference(constrained_superposition,[],[f1620,f1625])).
% 0.21/0.36 thf(f2178,plain,(
% 0.21/0.36 ( ! [X0 : (c > d)] : ((((member @ (c > d) @ X0 @ (carr_prodag @ c @ d @ module_ext @ d @ a @ e @ i @ m))) != $true) | (((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ X0 @ sK54)) = ((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ sK54 @ X0)))) )),
% 0.21/0.36 inference(trivial_inequality_removal,[],[f2175])).
% 0.21/0.36 thf(f2185,plain,(
% 0.21/0.36 ($true != $true) | (((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ sK54 @ (prod_zero @ c @ d @ module_ext @ d @ a @ e @ i @ m))) = ((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ (prod_zero @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ sK54)))),
% 0.21/0.36 inference(constrained_superposition,[],[f2178,f1623])).
% 0.21/0.36 thf(f2186,plain,(
% 0.21/0.36 (((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ sK54 @ (prod_zero @ c @ d @ module_ext @ d @ a @ e @ i @ m))) = ((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ (prod_zero @ c @ d @ module_ext @ d @ a @ e @ i @ m) @ sK54)))),
% 0.21/0.36 inference(trivial_inequality_removal,[],[f2185])).
% 0.21/0.36 thf(f2188,plain,(
% 0.21/0.36 (sK54 = ((prod_pOp @ c @ d @ module_ext @ d @ a @ e @ i @ m @ sK54 @ (prod_zero @ c @ d @ module_ext @ d @ a @ e @ i @ m))))),
% 0.21/0.36 inference(forward_demodulation,[],[f2186,f1972])).
% 0.21/0.36 thf(f2189,plain,(
% 0.21/0.36 $false),
% 0.21/0.36 inference(forward_subsumption_resolution,[],[f2188,f1626])).
% 0.21/0.36 % SZS output end Proof for theBenchmark
% 0.21/0.36 % (1750631)------------------------------
% 0.21/0.36 % (1750631)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (1750631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (1750631)CaDiCaL version: 2.1.3
% 0.21/0.36 % (1750631)Termination reason: Refutation
% 0.21/0.36 % (1750631)Time elapsed: 0.062 s
% 0.21/0.36 % (1750631)Peak memory usage: 14 MB
% 0.21/0.36 % (1750631)Instructions burned: 259 (million)
% 0.21/0.36 % (1750624)Success in time 0.127 s
% 0.21/0.36 % Vampire exiting
%------------------------------------------------------------------------------