%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP159^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:08:36 AM UTC 2026
% Result : Theorem 0.51s 0.41s
% Output : Refutation 0.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP159^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n009.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 20:04:00 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.21/0.28 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
% 0.51/0.41 % (284867)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.51/0.41 % (284876)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1020437470:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.51/0.41 % (284878)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.51/0.41 % (284878)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
% 0.51/0.41 % (284874)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2156915047:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.51/0.41 % (284873)lrs+10_16_si=on:nwc=1.5:random_seed=2614540867:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.51/0.41 % (284875)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=4024985308: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)
% 0.51/0.41 % (284876)Instruction limit reached!
% 0.51/0.41 % (284876)------------------------------
% 0.51/0.41 % (284876)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.41 % (284876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.41 % (284876)CaDiCaL version: 2.1.3
% 0.51/0.41 % (284876)Termination reason: Instruction limit
% 0.51/0.41 % (284876)Termination phase: Property scanning
% 0.51/0.41 % (284876)Time elapsed: 0.007 s
% 0.51/0.41 % (284876)Peak memory usage: 10 MB
% 0.51/0.41 % (284876)Instructions burned: 28 (million)
% 0.51/0.41 % (284878)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=2989107625:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.51/0.41 % (284877)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=32688667:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.51/0.41 % (284874)Instruction limit reached!
% 0.51/0.41 % (284874)------------------------------
% 0.51/0.41 % (284874)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.41 % (284874)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.41 % (284874)CaDiCaL version: 2.1.3
% 0.51/0.41 % (284874)Termination reason: Instruction limit
% 0.51/0.41 % (284874)Termination phase: shuffling
% 0.51/0.41 % (284874)Time elapsed: 0.003 s
% 0.51/0.41 % (284874)Peak memory usage: 10 MB
% 0.51/0.41 % (284874)Instructions burned: 4 (million)
% 0.51/0.41 % (284873)Instruction limit reached!
% 0.51/0.41 % (284873)------------------------------
% 0.51/0.41 % (284873)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.41 % (284873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.41 % (284873)CaDiCaL version: 2.1.3
% 0.51/0.41 % (284873)Termination reason: Instruction limit
% 0.51/0.41 % (284873)Termination phase: shuffling
% 0.51/0.41 % (284873)Time elapsed: 0.009 s
% 0.51/0.41 % (284873)Peak memory usage: 10 MB
% 0.51/0.41 % (284873)Instructions burned: 18 (million)
% 0.51/0.41 % (284872)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2149808479:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.51/0.41 % (284885)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3787378745:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.51/0.41 % (284885)Instruction limit reached!
% 0.51/0.41 % (284885)------------------------------
% 0.51/0.41 % (284885)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.41 % (284885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.41 % (284885)CaDiCaL version: 2.1.3
% 0.51/0.41 % (284885)Termination reason: Instruction limit
% 0.51/0.41 % (284885)Termination phase: shuffling
% 0.51/0.41 % (284885)Time elapsed: 0.001 s
% 0.51/0.41 % (284885)Peak memory usage: 10 MB
% 0.51/0.41 % (284885)Instructions burned: 3 (million)
% 0.51/0.41 % (284890)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3134885609:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.51/0.41 % (284890)Instruction limit reached!
% 0.51/0.41 % (284890)------------------------------
% 0.51/0.41 % (284890)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.41 % (284890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.41 % (284890)CaDiCaL version: 2.1.3
% 0.51/0.41 % (284890)Termination reason: Instruction limit
% 0.51/0.41 % (284890)Termination phase: shuffling
% 0.51/0.41 % (284890)Time elapsed: 0.003 s
% 0.51/0.41 % (284890)Peak memory usage: 10 MB
% 0.51/0.41 % (284890)Instructions burned: 13 (million)
% 0.51/0.41 % (284886)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=861091513:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.51/0.41 % (284892)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
% 0.51/0.41 % (284892)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.51/0.41 % (284887)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.51/0.41 % (284877)Instruction limit reached!
% 0.51/0.41 % (284877)------------------------------
% 0.51/0.41 % (284877)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.41 % (284877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.41 % (284877)CaDiCaL version: 2.1.3
% 0.51/0.41 % (284877)Termination reason: Instruction limit
% 0.51/0.41 % (284877)Termination phase: Property scanning
% 0.51/0.41 % (284877)Time elapsed: 0.038 s
% 0.51/0.41 % (284877)Peak memory usage: 12 MB
% 0.51/0.41 % (284877)Instructions burned: 77 (million)
% 0.51/0.41 % (284892)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3279178199:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.51/0.41 % (284886)Instruction limit reached!
% 0.51/0.41 % (284886)------------------------------
% 0.51/0.41 % (284886)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.41 % (284886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.41 % (284886)CaDiCaL version: 2.1.3
% 0.51/0.41 % (284887)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1244625259:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.51/0.41 % (284886)Termination reason: Instruction limit
% 0.51/0.41 % (284886)Termination phase: shuffling
% 0.51/0.41 % (284886)Time elapsed: 0.004 s
% 0.51/0.41 % (284886)Peak memory usage: 10 MB
% 0.51/0.41 % (284886)Instructions burned: 6 (million)
% 0.51/0.41 % (284887)Instruction limit reached!
% 0.51/0.41 % (284887)------------------------------
% 0.51/0.41 % (284887)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.41 % (284887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.41 % (284887)CaDiCaL version: 2.1.3
% 0.51/0.41 % (284887)Termination reason: Instruction limit
% 0.51/0.41 % (284887)Termination phase: shuffling
% 0.51/0.41 % (284887)Time elapsed: 0.004 s
% 0.51/0.41 % (284887)Peak memory usage: 10 MB
% 0.51/0.41 % (284887)Instructions burned: 8 (million)
% 0.51/0.41 % (284892)Instruction limit reached!
% 0.51/0.41 % (284892)------------------------------
% 0.51/0.41 % (284892)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.41 % (284892)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.41 % (284892)CaDiCaL version: 2.1.3
% 0.51/0.41 % (284892)Termination reason: Instruction limit
% 0.51/0.41 % (284892)Termination phase: shuffling
% 0.51/0.41 % (284892)Time elapsed: 0.007 s
% 0.51/0.41 % (284892)Peak memory usage: 10 MB
% 0.51/0.41 % (284892)Instructions burned: 28 (million)
% 0.51/0.41 % (284872)Instruction limit reached!
% 0.51/0.41 % (284872)------------------------------
% 0.51/0.41 % (284872)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.41 % (284872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.41 % (284872)CaDiCaL version: 2.1.3
% 0.51/0.41 % (284872)Termination reason: Instruction limit
% 0.51/0.41 % (284872)Termination phase: Property scanning
% 0.51/0.41 % (284872)Time elapsed: 0.043 s
% 0.51/0.41 % (284872)Peak memory usage: 11 MB
% 0.51/0.41 % (284872)Instructions burned: 87 (million)
% 0.51/0.41 % (284899)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1008465918:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.51/0.41 % (284895)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=2356027164:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.51/0.41 % (284897)lrs+10_1_si=on:cs=on:random_seed=3758778739:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.51/0.41 % (284898)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.51/0.41 % (284875) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-284867-284875"...
% 0.51/0.41 % (284897)Instruction limit reached!
% 0.51/0.41 % (284897)------------------------------
% 0.51/0.41 % (284897)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.41 % (284897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.41 % (284897)CaDiCaL version: 2.1.3
% 0.51/0.41 % (284897)Termination reason: Instruction limit
% 0.51/0.41 % (284897)Termination phase: shuffling
% 0.51/0.41 % (284897)Time elapsed: 0.004 s
% 0.51/0.41 % (284897)Peak memory usage: 10 MB
% 0.51/0.41 % (284897)Instructions burned: 8 (million)
% 0.51/0.41 % (284898)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=2381437632:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.51/0.41 % (284875)...printing done.
% 0.51/0.41 % (284898)Instruction limit reached!
% 0.51/0.41 % (284898)------------------------------
% 0.51/0.41 % (284898)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.41 % (284898)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.41 % (284898)CaDiCaL version: 2.1.3
% 0.51/0.41 % (284898)Termination reason: Instruction limit
% 0.51/0.41 % (284898)Termination phase: shuffling
% 0.51/0.41 % (284898)Time elapsed: 0.002 s
% 0.51/0.41 % (284898)Peak memory usage: 10 MB
% 0.51/0.41 % (284898)Instructions burned: 3 (million)
% 0.51/0.41 % (284875)Refutation found. Thanks to Tanya!
% 0.51/0.41 % SZS status Theorem for theBenchmark
% 0.51/0.41 % SZS output start Proof for theBenchmark
% 0.51/0.41 thf(type_def_5, type, refine1665802226e_nres: $tType > $tType).
% 0.51/0.41 thf(type_def_6, type, product_unit: $tType).
% 0.51/0.41 thf(type_def_7, type, product_prod: ($tType * $tType) > $tType).
% 0.51/0.41 thf(type_def_8, type, set: $tType > $tType).
% 0.51/0.41 thf(type_def_9, type, b: $tType).
% 0.51/0.41 thf(type_def_10, type, a: $tType).
% 0.51/0.41 thf(type_def_11, type, sTfun: ($tType * $tType) > $tType).
% 0.51/0.41 thf(func_def_0, type, bounded_lattice: !>[X0: $tType]:($o)).
% 0.51/0.41 thf(func_def_1, type, type: !>[X0: $tType]:($o)).
% 0.51/0.41 thf(func_def_2, type, ord: !>[X0: $tType]:($o)).
% 0.51/0.41 thf(func_def_3, type, top: !>[X0: $tType]:($o)).
% 0.51/0.41 thf(func_def_4, type, order: !>[X0: $tType]:($o)).
% 0.51/0.41 thf(func_def_5, type, linorder: !>[X0: $tType]:($o)).
% 0.51/0.41 thf(func_def_6, type, preorder: !>[X0: $tType]:($o)).
% 0.51/0.41 thf(func_def_7, type, order_top: !>[X0: $tType]:($o)).
% 0.51/0.41 thf(func_def_8, type, bounded_lattice_top: !>[X0: $tType]:($o)).
% 0.51/0.41 thf(func_def_9, type, comple187826305attice: !>[X0: $tType]:($o)).
% 0.51/0.41 thf(func_def_10, type, bNF_Ca1785829860lChain: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > (X0 > X1) > $o))).
% 0.51/0.41 thf(func_def_11, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.51/0.41 thf(func_def_12, type, sup_sup: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.51/0.41 thf(func_def_13, type, bijective: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > $o))).
% 0.51/0.41 thf(func_def_14, type, fun_of_rel: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > X0 > X1))).
% 0.51/0.41 thf(func_def_15, type, rel_restrict: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ X0 > set @ product_prod @ X0 @ X0))).
% 0.51/0.41 thf(func_def_16, type, uncurry: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.51/0.41 thf(func_def_17, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.51/0.41 thf(func_def_18, type, order_Greatest: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.51/0.41 thf(func_def_19, type, top_top: !>[X0: $tType]:(X0)).
% 0.51/0.41 thf(func_def_20, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.51/0.41 thf(func_def_21, type, refine1687780735RETURN: !>[X0: $tType]:((X0 > refine1665802226e_nres @ X0))).
% 0.51/0.41 thf(func_def_22, type, refine81118332bs_fun: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > refine1665802226e_nres @ X0 > refine1665802226e_nres @ X1))).
% 0.51/0.41 thf(func_def_23, type, refine463715084e_bind: !>[X0: $tType, X1: $tType]:((refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1))).
% 0.51/0.41 thf(func_def_24, type, refine1073749519nc_fun: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > refine1665802226e_nres @ X1 > refine1665802226e_nres @ X0))).
% 0.51/0.41 thf(func_def_25, type, refine1315500908_inres: !>[X0: $tType]:((refine1665802226e_nres @ X0 > X0 > $o))).
% 0.51/0.41 thf(func_def_26, type, refine406925620_inres: !>[X0: $tType]:((refine1665802226e_nres @ X0 > X0 > $o))).
% 0.51/0.41 thf(func_def_27, type, refine1102455758nofail: !>[X0: $tType]:((refine1665802226e_nres @ X0 > $o))).
% 0.51/0.41 thf(func_def_28, type, refine605929679le_RES: !>[X0: $tType]:((set @ X0 > refine1665802226e_nres @ X0))).
% 0.51/0.41 thf(func_def_29, type, refine1672542526he_RES: !>[X0: $tType]:((refine1665802226e_nres @ X0 > set @ X0))).
% 0.51/0.41 thf(func_def_30, type, domain: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > set @ X0))).
% 0.51/0.41 thf(func_def_31, type, id: !>[X0: $tType]:(set @ product_prod @ X0 @ X0)).
% 0.51/0.41 thf(func_def_32, type, image: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > set @ X0 > set @ X1))).
% 0.51/0.41 thf(func_def_33, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.51/0.41 thf(func_def_34, type, transitive_rtrancl: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ product_prod @ X0 @ X0))).
% 0.51/0.41 thf(func_def_35, type, transitive_trancl: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ product_prod @ X0 @ X0))).
% 0.51/0.41 thf(func_def_36, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.51/0.41 thf(func_def_37, type, r: set @ product_prod @ a @ b).
% 0.51/0.41 thf(func_def_38, type, x: refine1665802226e_nres @ a).
% 0.51/0.41 thf(func_def_42, type, db0: !>[X0: $tType]:(X0)).
% 0.51/0.41 thf(func_def_43, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.51/0.41 thf(func_def_44, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.51/0.41 thf(func_def_45, type, db2: !>[X0: $tType]:(X0)).
% 0.51/0.41 thf(func_def_46, type, db1: !>[X0: $tType]:(X0)).
% 0.51/0.41 thf(func_def_47, type, vIMP: ($o > $o > $o)).
% 0.51/0.41 thf(func_def_48, type, vAND: ($o > $o > $o)).
% 0.51/0.41 thf(func_def_49, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.51/0.41 thf(func_def_50, type, db3: !>[X0: $tType]:(X0)).
% 0.51/0.41 thf(func_def_51, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.51/0.41 thf(func_def_52, type, vNOT: ($o > $o)).
% 0.51/0.41 thf(func_def_53, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.51/0.41 thf(func_def_54, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.51/0.41 thf(func_def_55, type, sK2: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0))).
% 0.51/0.41 thf(func_def_56, type, sK3: !>[X0: $tType]:(((X0 > $o) > set @ X0 > set @ X0 > X0))).
% 0.51/0.41 thf(func_def_57, type, sK4: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 0.51/0.41 thf(func_def_58, type, sK5: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 0.51/0.41 thf(func_def_59, type, sK6: !>[X0: $tType]:((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > X0))).
% 0.51/0.41 thf(func_def_60, type, sK7: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1) > (X1 > X0) > (X2 > X0) > X2))).
% 0.51/0.41 thf(func_def_61, type, sK8: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.51/0.41 thf(func_def_62, type, sK9: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > (X1 > $o) > X0))).
% 0.51/0.41 thf(func_def_63, type, sK10: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > (X1 > $o) > X1))).
% 0.51/0.41 thf(func_def_64, type, sK11: !>[X0: $tType]:((set @ X0 > set @ X0 > set @ X0 > set @ X0))).
% 0.51/0.41 thf(func_def_65, type, sK12: !>[X0: $tType]:((set @ X0 > set @ X0 > set @ X0 > set @ X0))).
% 0.51/0.41 thf(func_def_66, type, sK13: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.51/0.41 thf(func_def_67, type, sK14: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.51/0.41 thf(func_def_68, type, sK15: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.51/0.41 thf(func_def_69, type, sK16: !>[X0: $tType]:((set @ X0 > X0))).
% 0.51/0.41 thf(func_def_70, type, sK17: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.51/0.41 thf(func_def_71, type, sK18: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > (X0 > X1 > $o) > X0))).
% 0.51/0.41 thf(func_def_72, type, sK19: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > (X0 > X1 > $o) > X1))).
% 0.51/0.41 thf(func_def_73, type, sK20: !>[X0: $tType, X1: $tType]:((refine1665802226e_nres @ X1 > set @ product_prod @ X1 @ X0 > X1))).
% 0.51/0.41 thf(func_def_74, type, sK21: !>[X0: $tType]:(((X0 > $o) > X0 > X0))).
% 0.51/0.41 thf(func_def_75, type, sK22: !>[X0: $tType]:((set @ X0 > X0))).
% 0.51/0.41 thf(func_def_76, type, sK23: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ X1 > set @ X0 > X1))).
% 0.51/0.41 thf(func_def_77, type, sK24: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.51/0.41 thf(func_def_78, type, sK25: !>[X0: $tType]:((X0 > set @ product_prod @ X0 @ X0 > X0 > X0))).
% 0.51/0.41 thf(func_def_79, type, sK26: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.51/0.41 thf(func_def_80, type, sK27: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.51/0.41 thf(func_def_81, type, sK28: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > X0 > X1))).
% 0.51/0.41 thf(func_def_82, type, sK29: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 0.51/0.41 thf(func_def_83, type, sK30: !>[X0: $tType, X1: $tType]:((refine1665802226e_nres @ X1 > (X1 > refine1665802226e_nres @ X0) > X1))).
% 0.51/0.41 thf(func_def_84, type, sK31: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.51/0.41 thf(func_def_85, type, sK32: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.51/0.41 thf(func_def_86, type, sK33: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.51/0.41 thf(func_def_87, type, sK34: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.51/0.41 thf(func_def_88, type, sK35: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > refine1665802226e_nres @ X0 > X1 > X0))).
% 0.51/0.41 thf(func_def_89, type, sK36: !>[X0: $tType, X1: $tType]:(((X0 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X1) > X0))).
% 0.51/0.41 thf(func_def_90, type, sK37: !>[X0: $tType, X1: $tType]:((X1 > set @ product_prod @ X1 @ X0 > X0))).
% 0.51/0.41 thf(func_def_91, type, sK38: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 0.51/0.41 thf(func_def_92, type, sK39: !>[X0: $tType]:((refine1665802226e_nres @ X0 > set @ X0))).
% 0.51/0.41 thf(func_def_93, type, sK40: !>[X0: $tType]:((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > X0))).
% 0.51/0.41 thf(func_def_94, type, sK41: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.51/0.41 thf(func_def_95, type, sK42: !>[X0: $tType, X1: $tType]:(((X1 > refine1665802226e_nres @ X0) > (X1 > refine1665802226e_nres @ X0) > refine1665802226e_nres @ X1 > X1))).
% 0.51/0.41 thf(func_def_96, type, sK43: !>[X0: $tType, X1: $tType]:((((X0 > X1) > product_prod @ X0 @ X0 > $o) > X0))).
% 0.51/0.41 thf(func_def_97, type, sK44: !>[X0: $tType, X1: $tType]:((((X0 > X1) > product_prod @ X0 @ X0 > $o) > X0 > X1))).
% 0.51/0.41 thf(func_def_98, type, sK45: !>[X0: $tType, X1: $tType]:((((X0 > X1) > product_prod @ X0 @ X0 > $o) > X0))).
% 0.51/0.41 thf(func_def_99, type, sK46: !>[X0: $tType, X1: $tType]:((product_prod @ (X0 > X1) @ product_prod @ X0 @ X0 > X0))).
% 0.51/0.41 thf(func_def_100, type, sK47: !>[X0: $tType, X1: $tType]:((product_prod @ (X0 > X1) @ product_prod @ X0 @ X0 > X0))).
% 0.51/0.41 thf(func_def_101, type, sK48: !>[X0: $tType, X1: $tType]:((product_prod @ (X0 > X1) @ product_prod @ X0 @ X0 > X0 > X1))).
% 0.51/0.41 thf(func_def_102, type, sK49: !>[X0: $tType]:((X0 > X0 > set @ product_prod @ X0 @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 0.51/0.41 thf(func_def_103, type, sK50: !>[X0: $tType]:((X0 > X0 > set @ product_prod @ X0 @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 0.51/0.41 thf(func_def_104, type, sK51: !>[X0: $tType, X1: $tType]:((X0 > set @ product_prod @ X0 @ X1 > X1))).
% 0.51/0.41 thf(func_def_105, type, sK52: !>[X0: $tType, X1: $tType]:((X0 > set @ product_prod @ X0 @ X1 > X0))).
% 0.51/0.41 thf(func_def_106, type, sK53: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.51/0.41 thf(func_def_107, type, sK54: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.51/0.41 thf(func_def_108, type, sK55: !>[X0: $tType, X1: $tType]:((X1 > set @ product_prod @ X1 @ X0 > X0))).
% 0.51/0.41 thf(func_def_109, type, sK56: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.51/0.41 thf(func_def_110, type, sK57: !>[X0: $tType]:(((X0 > $o) > set @ X0 > set @ X0 > X0))).
% 0.51/0.41 thf(func_def_111, type, sK58: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 0.51/0.41 thf(func_def_112, type, sK59: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 0.51/0.41 thf(func_def_113, type, sK60: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.51/0.41 thf(func_def_114, type, sK61: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.51/0.41 thf(func_def_115, type, sK62: !>[X0: $tType, X1: $tType]:(((X0 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X0 > refine1665802226e_nres @ X1 > X0))).
% 0.51/0.41 thf(func_def_116, type, sK63: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.51/0.41 thf(func_def_117, type, sK64: !>[X0: $tType]:((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > X0))).
% 0.51/0.41 thf(func_def_118, type, sK65: !>[X0: $tType]:(X0)).
% 0.51/0.41 thf(func_def_119, type, sK66: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > set @ product_prod @ X0 @ X1 > X1))).
% 0.51/0.41 thf(func_def_120, type, sK67: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > set @ product_prod @ X0 @ X1 > X0))).
% 0.51/0.41 thf(func_def_121, type, sK68: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.51/0.41 thf(func_def_122, type, sK69: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.51/0.41 thf(func_def_123, type, sK70: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.51/0.41 thf(func_def_124, type, sK71: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.51/0.41 thf(func_def_125, type, sK72: !>[X0: $tType, X1: $tType]:((refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1 > X0))).
% 0.51/0.41 thf(f4,axiom,(
% 0.51/0.41 ! [X1 : $tType,X0 : $tType,X2 : set @ product_prod @ X1 @ X0] : (((refine1073749519nc_fun @ X1 @ X0 @ X2 @ top_top @ refine1665802226e_nres @ X0)) = top_top @ refine1665802226e_nres @ X1)),
% 0.51/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_conc__fun__FAIL)).
% 0.51/0.41 thf(f5,axiom,(
% 0.51/0.41 ! [X0 : $tType,X1 : refine1665802226e_nres @ X0] : (ord_less_eq @ refine1665802226e_nres @ X0 @ X1 @ top_top @ refine1665802226e_nres @ X0)),
% 0.51/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_nres__order__simps_I3_J)).
% 0.51/0.41 thf(f299,conjecture,(
% 0.51/0.41 (ord_less_eq @ refine1665802226e_nres @ a @ x @ (refine1073749519nc_fun @ a @ b @ r @ top_top @ refine1665802226e_nres @ b))),
% 0.51/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.51/0.41 thf(f300,negated_conjecture,(
% 0.51/0.41 ~(ord_less_eq @ refine1665802226e_nres @ a @ x @ (refine1073749519nc_fun @ a @ b @ r @ top_top @ refine1665802226e_nres @ b))),
% 0.51/0.41 inference(negated_conjecture,[status(cth)],[f299])).
% 0.51/0.41 thf(f486,plain,(
% 0.51/0.41 ! [X0 : $tType,X1 : refine1665802226e_nres @ X0] : (ord_less_eq @ refine1665802226e_nres @ X0 @ X1 @ top_top @ refine1665802226e_nres @ X0)),
% 0.51/0.41 inference(rectify,[],[f5])).
% 0.51/0.41 thf(f487,plain,(
% 0.51/0.41 ! [X0 : $tType,X1 : refine1665802226e_nres @ X0] : (((ord_less_eq @ refine1665802226e_nres @ X0 @ X1 @ top_top @ refine1665802226e_nres @ X0)) = $true)),
% 0.51/0.41 inference(fool_elimination,[],[f486])).
% 0.51/0.41 thf(f494,plain,(
% 0.51/0.41 ~(ord_less_eq @ refine1665802226e_nres @ a @ x @ (refine1073749519nc_fun @ a @ b @ r @ top_top @ refine1665802226e_nres @ b))),
% 0.51/0.41 inference(rectify,[],[f300])).
% 0.51/0.41 thf(f495,plain,(
% 0.51/0.41 ~ (((ord_less_eq @ refine1665802226e_nres @ a @ x @ (refine1073749519nc_fun @ a @ b @ r @ top_top @ refine1665802226e_nres @ b))) = $true)),
% 0.51/0.41 inference(fool_elimination,[],[f494])).
% 0.51/0.41 thf(f809,plain,(
% 0.51/0.41 (((ord_less_eq @ refine1665802226e_nres @ a @ x @ (refine1073749519nc_fun @ a @ b @ r @ top_top @ refine1665802226e_nres @ b))) != $true)),
% 0.51/0.41 inference(flattening,[],[f495])).
% 0.51/0.41 thf(f1129,plain,(
% 0.51/0.41 ! [X0 : $tType,X1 : $tType,X2 : set @ product_prod @ X0 @ X1] : (top_top @ refine1665802226e_nres @ X0 = ((refine1073749519nc_fun @ X0 @ X1 @ X2 @ top_top @ refine1665802226e_nres @ X1)))),
% 0.51/0.41 inference(rectify,[],[f4])).
% 0.51/0.41 thf(f1419,plain,(
% 0.51/0.41 ( ! [X1 : $tType,X0 : $tType,X2 : set @ product_prod @ X0 @ X1] : ((top_top @ refine1665802226e_nres @ X0 = ((refine1073749519nc_fun @ X0 @ X1 @ X2 @ top_top @ refine1665802226e_nres @ X1)))) )),
% 0.51/0.41 inference(cnf_transformation,[],[f1129])).
% 0.51/0.41 thf(f1573,plain,(
% 0.51/0.41 (((ord_less_eq @ refine1665802226e_nres @ a @ x @ (refine1073749519nc_fun @ a @ b @ r @ top_top @ refine1665802226e_nres @ b))) != $true)),
% 0.51/0.41 inference(cnf_transformation,[],[f809])).
% 0.51/0.41 thf(f1617,plain,(
% 0.51/0.41 ( ! [X0 : $tType,X1 : refine1665802226e_nres @ X0] : ((((ord_less_eq @ refine1665802226e_nres @ X0 @ X1 @ top_top @ refine1665802226e_nres @ X0)) = $true)) )),
% 0.51/0.41 inference(cnf_transformation,[],[f487])).
% 0.51/0.41 thf(f1890,definition,(
% 0.51/0.41 spl73_12 <=> (((ord_less_eq @ refine1665802226e_nres @ a @ x @ (refine1073749519nc_fun @ a @ b @ r @ top_top @ refine1665802226e_nres @ b))) = $true)),
% 0.51/0.41 introduced(definition,[new_symbols(definition,[spl73_12])],[avatar_definition])).
% 0.51/0.41 thf(f1892,plain,(
% 0.51/0.41 (((ord_less_eq @ refine1665802226e_nres @ a @ x @ (refine1073749519nc_fun @ a @ b @ r @ top_top @ refine1665802226e_nres @ b))) != $true) | spl73_12),
% 0.51/0.41 inference(avatar_component_clause,[],[f1890])).
% 0.51/0.41 thf(f1893,plain,(
% 0.51/0.41 ~spl73_12),
% 0.51/0.41 inference(avatar_split_clause,[],[f1573,f1890])).
% 0.51/0.41 thf(f1931,plain,(
% 0.51/0.41 (((ord_less_eq @ refine1665802226e_nres @ a @ x @ top_top @ refine1665802226e_nres @ a)) != $true) | spl73_12),
% 0.51/0.41 inference(superposition,[],[f1892,f1419])).
% 0.51/0.41 thf(f1932,plain,(
% 0.51/0.41 $false | spl73_12),
% 0.51/0.41 inference(forward_subsumption_resolution,[],[f1931,f1617])).
% 0.51/0.41 thf(f1933,plain,(
% 0.51/0.41 spl73_12),
% 0.51/0.41 inference(avatar_contradiction_clause,[],[f1932])).
% 0.51/0.41 cnf(s12, plain, ~spl73_12, inference(sat_conversion,[],[f1893])).
% 0.51/0.41 cnf(s20, plain, spl73_12, inference(sat_conversion,[],[f1933])).
% 0.51/0.41 cnf(s21, plain, $false, inference(rat,[],[s12,s20])).
% 0.51/0.41 thf(f1934,plain,(
% 0.51/0.41 $false),
% 0.51/0.41 inference(avatar_sat_refutation,[],[s21])).
% 0.51/0.41 % SZS output end Proof for theBenchmark
% 0.51/0.41 % (284875)------------------------------
% 0.51/0.41 % (284875)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.41 % (284875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.41 % (284875)CaDiCaL version: 2.1.3
% 0.51/0.41 % (284875)Termination reason: Refutation
% 0.51/0.41 % (284875)Time elapsed: 0.065 s
% 0.51/0.41 % (284875)Peak memory usage: 14 MB
% 0.51/0.41 % (284875)Instructions burned: 132 (million)
% 0.51/0.41 % (284867)Success in time 0.122 s
% 0.51/0.41 % Vampire exiting
%------------------------------------------------------------------------------