%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT246^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:48:37 AM UTC 2026
% Result : Theorem 0.61s 0.42s
% Output : Refutation 0.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT246^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n004.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 18:14:37 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.21/0.27 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
% 0.61/0.42 % (1647410)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.61/0.42 % (1647417)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3415893469:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.61/0.42 % (1647417)Instruction limit reached!
% 0.61/0.42 % (1647417)------------------------------
% 0.61/0.42 % (1647417)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (1647417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (1647417)CaDiCaL version: 2.1.3
% 0.61/0.42 % (1647417)Termination reason: Instruction limit
% 0.61/0.42 % (1647417)Termination phase: shuffling
% 0.61/0.42 % (1647417)Time elapsed: 0.003 s
% 0.61/0.42 % (1647417)Peak memory usage: 10 MB
% 0.61/0.42 % (1647417)Instructions burned: 10 (million)
% 0.61/0.42 % (1647415)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1065202261:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.61/0.42 % (1647416)lrs+10_16_si=on:nwc=1.5:random_seed=3660188475:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.61/0.42 % (1647418)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=2427348538: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)
% 0.61/0.42 % (1647420)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=65519701:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.61/0.42 % (1647423)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=218649866:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.61/0.42 % (1647423)Instruction limit reached!
% 0.61/0.42 % (1647423)------------------------------
% 0.61/0.42 % (1647423)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (1647423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (1647423)CaDiCaL version: 2.1.3
% 0.61/0.42 % (1647423)Termination reason: Instruction limit
% 0.61/0.42 % (1647423)Termination phase: shuffling
% 0.61/0.42 % (1647423)Time elapsed: 0.001 s
% 0.61/0.42 % (1647423)Peak memory usage: 10 MB
% 0.61/0.42 % (1647423)Instructions burned: 2 (million)
% 0.61/0.42 % (1647416)Instruction limit reached!
% 0.61/0.42 % (1647416)------------------------------
% 0.61/0.42 % (1647416)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (1647416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (1647416)CaDiCaL version: 2.1.3
% 0.61/0.42 % (1647416)Termination reason: Instruction limit
% 0.61/0.42 % (1647416)Termination phase: Property scanning
% 0.61/0.42 % (1647416)Time elapsed: 0.009 s
% 0.61/0.42 % (1647416)Peak memory usage: 10 MB
% 0.61/0.42 % (1647416)Instructions burned: 19 (million)
% 0.61/0.42 % (1647421)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.61/0.42 % (1647421)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
% 0.61/0.42 % (1647419)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1861668981:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.61/0.42 % (1647421)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=4227594250:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.61/0.42 % (1647429)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2637499069:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.61/0.42 % (1647429)Instruction limit reached!
% 0.61/0.42 % (1647429)------------------------------
% 0.61/0.42 % (1647429)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (1647429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (1647429)CaDiCaL version: 2.1.3
% 0.61/0.42 % (1647429)Termination reason: Instruction limit
% 0.61/0.42 % (1647429)Termination phase: shuffling
% 0.61/0.42 % (1647429)Time elapsed: 0.002 s
% 0.61/0.42 % (1647429)Peak memory usage: 10 MB
% 0.61/0.42 % (1647429)Instructions burned: 9 (million)
% 0.61/0.42 % (1647430)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.61/0.42 % (1647430)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=860245623:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.61/0.42 % (1647434)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2785013658:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.61/0.42 % (1647430)Instruction limit reached!
% 0.61/0.42 % (1647430)------------------------------
% 0.61/0.42 % (1647430)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (1647430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (1647430)CaDiCaL version: 2.1.3
% 0.61/0.42 % (1647430)Termination reason: Instruction limit
% 0.61/0.42 % (1647430)Termination phase: shuffling
% 0.61/0.42 % (1647430)Time elapsed: 0.004 s
% 0.61/0.42 % (1647430)Peak memory usage: 10 MB
% 0.61/0.42 % (1647430)Instructions burned: 8 (million)
% 0.61/0.42 % (1647434)Instruction limit reached!
% 0.61/0.42 % (1647434)------------------------------
% 0.61/0.42 % (1647434)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (1647434)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (1647434)CaDiCaL version: 2.1.3
% 0.61/0.42 % (1647419)Instruction limit reached!
% 0.61/0.42 % (1647419)------------------------------
% 0.61/0.42 % (1647419)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (1647419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (1647419)CaDiCaL version: 2.1.3
% 0.61/0.42 % (1647419)Termination reason: Instruction limit
% 0.61/0.42 % (1647419)Termination phase: Property scanning
% 0.61/0.42 % (1647419)Time elapsed: 0.022 s
% 0.61/0.42 % (1647419)Peak memory usage: 10 MB
% 0.61/0.42 % (1647419)Instructions burned: 25 (million)
% 0.61/0.42 % (1647434)Termination reason: Instruction limit
% 0.61/0.42 % (1647434)Termination phase: shuffling
% 0.61/0.42 % (1647434)Time elapsed: 0.004 s
% 0.61/0.42 % (1647434)Peak memory usage: 10 MB
% 0.61/0.42 % (1647434)Instructions burned: 16 (million)
% 0.61/0.42 % (1647420)Instruction limit reached!
% 0.61/0.42 % (1647420)------------------------------
% 0.61/0.42 % (1647420)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (1647420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (1647420)CaDiCaL version: 2.1.3
% 0.61/0.42 % (1647420)Termination reason: Instruction limit
% 0.61/0.42 % (1647420)Termination phase: Function definition elimination
% 0.61/0.42 % (1647420)Time elapsed: 0.035 s
% 0.61/0.42 % (1647420)Peak memory usage: 12 MB
% 0.61/0.42 % (1647420)Instructions burned: 76 (million)
% 0.61/0.42 % (1647415)Instruction limit reached!
% 0.61/0.42 % (1647415)------------------------------
% 0.61/0.42 % (1647415)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (1647415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (1647415)CaDiCaL version: 2.1.3
% 0.61/0.42 % (1647415)Termination reason: Instruction limit
% 0.61/0.42 % (1647415)Termination phase: Property scanning
% 0.61/0.42 % (1647415)Time elapsed: 0.041 s
% 0.61/0.42 % (1647415)Peak memory usage: 12 MB
% 0.61/0.42 % (1647415)Instructions burned: 89 (million)
% 0.61/0.42 % (1647437)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
% 0.61/0.42 % (1647437)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.61/0.42 % (1647437)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=4124917598:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.61/0.42 % (1647440)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.61/0.42 % (1647437)Instruction limit reached!
% 0.61/0.42 % (1647437)------------------------------
% 0.61/0.42 % (1647437)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (1647437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (1647437)CaDiCaL version: 2.1.3
% 0.61/0.42 % (1647437)Termination reason: Instruction limit
% 0.61/0.42 % (1647437)Termination phase: shuffling
% 0.61/0.42 % (1647437)Time elapsed: 0.007 s
% 0.61/0.42 % (1647437)Peak memory usage: 10 MB
% 0.61/0.42 % (1647437)Instructions burned: 31 (million)
% 0.61/0.42 % (1647440)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=106464658:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.61/0.42 % (1647440)Instruction limit reached!
% 0.61/0.42 % (1647440)------------------------------
% 0.61/0.42 % (1647440)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (1647440)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (1647440)CaDiCaL version: 2.1.3
% 0.61/0.42 % (1647440)Termination reason: Instruction limit
% 0.61/0.42 % (1647440)Termination phase: shuffling
% 0.61/0.42 % (1647440)Time elapsed: 0.003 s
% 0.61/0.42 % (1647440)Peak memory usage: 10 MB
% 0.61/0.42 % (1647440)Instructions burned: 5 (million)
% 0.61/0.42 % (1647441)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=4206207725:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.61/0.42 % (1647443)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1688487663:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.61/0.42 % (1647439)lrs+10_1_si=on:cs=on:random_seed=3625609877:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.61/0.42 % (1647438)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=2757830658:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.61/0.42 % (1647445)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=4294260934:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.61/0.42 % (1647443) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1647410-1647443"...
% 0.61/0.42 % (1647443)...printing done.
% 0.61/0.42 % (1647441)Instruction limit reached!
% 0.61/0.42 % (1647441)------------------------------
% 0.61/0.42 % (1647441)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (1647441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (1647441)CaDiCaL version: 2.1.3
% 0.61/0.42 % (1647441)Termination reason: Instruction limit
% 0.61/0.42 % (1647441)Termination phase: Property scanning
% 0.61/0.42 % (1647441)Time elapsed: 0.018 s
% 0.61/0.42 % (1647441)Peak memory usage: 11 MB
% 0.61/0.42 % (1647441)Instructions burned: 38 (million)
% 0.61/0.42 % (1647443)Refutation found. Thanks to Tanya!
% 0.61/0.42 % SZS status Theorem for theBenchmark
% 0.61/0.42 % SZS output start Proof for theBenchmark
% 0.61/0.42 thf(type_def_5, type, stream170649215stream: $tType > $tType).
% 0.61/0.42 thf(type_def_6, type, list: $tType > $tType).
% 0.61/0.42 thf(type_def_7, type, nat: $tType).
% 0.61/0.42 thf(type_def_8, type, itself: $tType > $tType).
% 0.61/0.42 thf(type_def_9, type, a: $tType).
% 0.61/0.42 thf(type_def_10, type, sTfun: ($tType * $tType) > $tType).
% 0.61/0.42 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.42 thf(func_def_1, type, zero: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.42 thf(func_def_2, type, minus: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.42 thf(func_def_3, type, ord: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.42 thf(func_def_4, type, order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.42 thf(func_def_5, type, group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.42 thf(func_def_6, type, no_bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.42 thf(func_def_7, type, no_top: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.42 thf(func_def_8, type, linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.42 thf(func_def_9, type, preorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.42 thf(func_def_10, type, wellorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.42 thf(func_def_11, type, dense_order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.42 thf(func_def_12, type, dense_linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.42 thf(func_def_13, type, ordered_ab_group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.42 thf(func_def_14, type, cancel146912293up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.42 thf(func_def_15, type, canoni770627133id_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.42 thf(func_def_16, type, condit1656338222tinuum: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.42 thf(func_def_17, type, condit1037483654norder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.42 thf(func_def_18, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.61/0.42 thf(func_def_19, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.61/0.42 thf(func_def_20, type, hilbert_GreatestM: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > $o) > X0))).
% 0.61/0.42 thf(func_def_21, type, count_list: !>[X0: $tType]:((list @ X0 > X0 > nat))).
% 0.61/0.42 thf(func_def_22, type, linorder_sorted: !>[X0: $tType]:((list @ X0 > $o))).
% 0.61/0.42 thf(func_def_23, type, tl: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 0.61/0.42 thf(func_def_24, type, list_ex: !>[X0: $tType]:(((X0 > $o) > list @ X0 > $o))).
% 0.61/0.42 thf(func_def_25, type, nth: !>[X0: $tType]:((list @ X0 > nat > X0))).
% 0.61/0.42 thf(func_def_26, type, remdups_adj: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 0.61/0.42 thf(func_def_27, type, rev: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 0.61/0.42 thf(func_def_28, type, takeWhile: !>[X0: $tType]:(((X0 > $o) > list @ X0 > list @ X0))).
% 0.61/0.42 thf(func_def_29, type, suc: (nat > nat)).
% 0.61/0.42 thf(func_def_30, type, size_size: !>[X0: $tType]:((X0 > nat))).
% 0.61/0.42 thf(func_def_31, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.61/0.42 thf(func_def_32, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.61/0.42 thf(func_def_33, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.61/0.42 thf(func_def_34, type, stream1035003186_shift: !>[X0: $tType]:((list @ X0 > stream170649215stream @ X0 > stream170649215stream @ X0))).
% 0.61/0.42 thf(func_def_35, type, stream370371455e_snth: !>[X0: $tType]:((stream170649215stream @ X0 > nat > X0))).
% 0.61/0.42 thf(func_def_36, type, n: nat).
% 0.61/0.42 thf(func_def_37, type, s: stream170649215stream @ a).
% 0.61/0.42 thf(func_def_38, type, xs: list @ a).
% 0.61/0.42 thf(func_def_42, type, vAND: ($o > $o > $o)).
% 0.61/0.42 thf(func_def_43, type, db1: !>[X0: $tType]:(X0)).
% 0.61/0.42 thf(func_def_44, type, db0: !>[X0: $tType]:(X0)).
% 0.61/0.42 thf(func_def_45, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.61/0.42 thf(func_def_46, type, vNOT: ($o > $o)).
% 0.61/0.42 thf(func_def_47, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.61/0.42 thf(func_def_48, type, db2: !>[X0: $tType]:(X0)).
% 0.61/0.42 thf(func_def_49, type, vOR: ($o > $o > $o)).
% 0.61/0.42 thf(func_def_50, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.61/0.42 thf(func_def_51, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.61/0.42 thf(func_def_52, type, vIMP: ($o > $o > $o)).
% 0.61/0.42 thf(func_def_53, type, sK0: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.61/0.42 thf(func_def_54, type, sK1: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.61/0.42 thf(func_def_55, type, sK2: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 0.61/0.42 thf(func_def_56, type, sK3: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.61/0.42 thf(func_def_57, type, sK4: !>[X0: $tType]:((nat > list @ X0))).
% 0.61/0.42 thf(func_def_58, type, sK5: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.61/0.42 thf(func_def_59, type, sK6: !>[X0: $tType]:((list @ X0 > list @ X0 > nat))).
% 0.61/0.42 thf(func_def_60, type, sK7: !>[X0: $tType]:(((X0 > nat) > nat > (X0 > $o) > X0))).
% 0.61/0.42 thf(func_def_61, type, sK8: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.61/0.42 thf(func_def_62, type, sK9: ((nat > nat) > nat)).
% 0.61/0.42 thf(func_def_63, type, sK10: ((nat > nat) > nat)).
% 0.61/0.42 thf(func_def_64, type, sK11: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.61/0.42 thf(func_def_65, type, sK12: ((nat > $o) > nat)).
% 0.61/0.42 thf(func_def_66, type, sK13: ((nat > $o) > nat)).
% 0.61/0.42 thf(func_def_67, type, sK14: ((nat > nat > $o) > nat)).
% 0.61/0.42 thf(func_def_68, type, sK15: ((nat > nat > $o) > nat)).
% 0.61/0.42 thf(func_def_69, type, sK16: ((nat > $o) > nat)).
% 0.61/0.42 thf(f2,axiom,(
% 0.61/0.42 ! [X0 : $tType,X2 : list @ X0,X3 : stream170649215stream @ X0,X1 : nat] : ((ord_less @ nat @ X1 @ (size_size @ list @ X0 @ X2)) => (((stream370371455e_snth @ X0 @ (stream1035003186_shift @ X0 @ X2 @ X3) @ X1)) = ((nth @ X0 @ X2 @ X1))))),
% 0.61/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_shift__snth__less)).
% 0.61/0.42 thf(f14,axiom,(
% 0.61/0.42 ! [X0 : $tType,X3 : stream170649215stream @ X0,X2 : nat,X1 : list @ X0] : ((ord_less_eq @ nat @ (size_size @ list @ X0 @ X1) @ X2) => (((stream370371455e_snth @ X0 @ (stream1035003186_shift @ X0 @ X1 @ X3) @ X2)) = ((stream370371455e_snth @ X0 @ X3 @ (minus_minus @ nat @ X2 @ (size_size @ list @ X0 @ X1))))))),
% 0.61/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_shift__snth__ge)).
% 0.61/0.42 thf(f16,axiom,(
% 0.61/0.42 ! [X0 : nat] : (ord_less_eq @ nat @ X0 @ X0)),
% 0.61/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_le__refl)).
% 0.61/0.42 thf(f20,axiom,(
% 0.61/0.42 ! [X1 : nat,X0 : nat] : ((ord_less_eq @ nat @ X1 @ X0) | (ord_less_eq @ nat @ X0 @ X1))),
% 0.61/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_nat__le__linear)).
% 0.61/0.42 thf(f26,axiom,(
% 0.61/0.42 ! [X1 : nat,X0 : nat] : ((ord_less_eq @ nat @ X0 @ X1) => ((X0 != X1) => (ord_less @ nat @ X0 @ X1)))),
% 0.61/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_le__neq__implies__less)).
% 0.61/0.42 thf(f275,conjecture,(
% 0.61/0.42 ((ord_less @ nat @ n @ (size_size @ list @ a @ xs)) => (((stream370371455e_snth @ a @ (stream1035003186_shift @ a @ xs @ s) @ n)) = ((nth @ a @ xs @ n)))) & (~(ord_less @ nat @ n @ (size_size @ list @ a @ xs)) => (((stream370371455e_snth @ a @ (stream1035003186_shift @ a @ xs @ s) @ n)) = ((stream370371455e_snth @ a @ s @ (minus_minus @ nat @ n @ (size_size @ list @ a @ xs))))))),
% 0.61/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.61/0.42 thf(f276,negated_conjecture,(
% 0.61/0.42 ~(((ord_less @ nat @ n @ (size_size @ list @ a @ xs)) => (((stream370371455e_snth @ a @ (stream1035003186_shift @ a @ xs @ s) @ n)) = ((nth @ a @ xs @ n)))) & (~(ord_less @ nat @ n @ (size_size @ list @ a @ xs)) => (((stream370371455e_snth @ a @ (stream1035003186_shift @ a @ xs @ s) @ n)) = ((stream370371455e_snth @ a @ s @ (minus_minus @ nat @ n @ (size_size @ list @ a @ xs)))))))),
% 0.61/0.42 inference(negated_conjecture,[status(cth)],[f275])).
% 0.61/0.42 thf(f324,plain,(
% 0.61/0.42 ! [X0 : $tType,X1 : stream170649215stream @ X0,X2 : nat,X3 : list @ X0] : ((ord_less_eq @ nat @ (size_size @ list @ X0 @ X3) @ X2) => (((stream370371455e_snth @ X0 @ X1 @ (minus_minus @ nat @ X2 @ (size_size @ list @ X0 @ X3)))) = ((stream370371455e_snth @ X0 @ (stream1035003186_shift @ X0 @ X3 @ X1) @ X2))))),
% 0.61/0.42 inference(rectify,[],[f14])).
% 0.61/0.42 thf(f325,plain,(
% 0.61/0.42 ! [X0 : $tType,X3 : list @ X0,X2 : nat,X1 : stream170649215stream @ X0] : ((((ord_less_eq @ nat @ (size_size @ list @ X0 @ X3) @ X2)) = $true) => (((stream370371455e_snth @ X0 @ X1 @ (minus_minus @ nat @ X2 @ (size_size @ list @ X0 @ X3)))) = ((stream370371455e_snth @ X0 @ (stream1035003186_shift @ X0 @ X3 @ X1) @ X2))))),
% 0.61/0.42 inference(fool_elimination,[],[f324])).
% 0.61/0.42 thf(f468,plain,(
% 0.61/0.42 ! [X0 : nat,X1 : nat] : ((ord_less_eq @ nat @ X0 @ X1) | (ord_less_eq @ nat @ X1 @ X0))),
% 0.61/0.42 inference(rectify,[],[f20])).
% 0.61/0.42 thf(f469,plain,(
% 0.61/0.42 ! [X0 : nat,X1 : nat] : ((((ord_less_eq @ nat @ X0 @ X1)) = $true) | (((ord_less_eq @ nat @ X1 @ X0)) = $true))),
% 0.61/0.42 inference(fool_elimination,[],[f468])).
% 0.61/0.42 thf(f484,plain,(
% 0.61/0.42 ! [X0 : nat] : (ord_less_eq @ nat @ X0 @ X0)),
% 0.61/0.42 inference(rectify,[],[f16])).
% 0.61/0.42 thf(f485,plain,(
% 0.61/0.42 ! [X0 : nat] : (((ord_less_eq @ nat @ X0 @ X0)) = $true)),
% 0.61/0.42 inference(fool_elimination,[],[f484])).
% 0.61/0.42 thf(f590,plain,(
% 0.61/0.42 ! [X0 : $tType,X1 : list @ X0,X2 : stream170649215stream @ X0,X3 : nat] : ((ord_less @ nat @ X3 @ (size_size @ list @ X0 @ X1)) => (((nth @ X0 @ X1 @ X3)) = ((stream370371455e_snth @ X0 @ (stream1035003186_shift @ X0 @ X1 @ X2) @ X3))))),
% 0.61/0.42 inference(rectify,[],[f2])).
% 0.61/0.42 thf(f591,plain,(
% 0.61/0.42 ! [X0 : $tType,X1 : list @ X0,X2 : stream170649215stream @ X0,X3 : nat] : ((((ord_less @ nat @ X3 @ (size_size @ list @ X0 @ X1))) = $true) => (((nth @ X0 @ X1 @ X3)) = ((stream370371455e_snth @ X0 @ (stream1035003186_shift @ X0 @ X1 @ X2) @ X3))))),
% 0.61/0.42 inference(fool_elimination,[],[f590])).
% 0.61/0.42 thf(f658,plain,(
% 0.61/0.42 ! [X0 : nat,X1 : nat] : ((ord_less_eq @ nat @ X1 @ X0) => ((X0 != X1) => (ord_less @ nat @ X1 @ X0)))),
% 0.61/0.42 inference(rectify,[],[f26])).
% 0.61/0.42 thf(f659,plain,(
% 0.61/0.42 ! [X1 : nat,X0 : nat] : ((((ord_less_eq @ nat @ X1 @ X0)) = $true) => ((X0 != X1) => (((ord_less @ nat @ X1 @ X0)) = $true)))),
% 0.61/0.42 inference(fool_elimination,[],[f658])).
% 0.61/0.42 thf(f780,plain,(
% 0.61/0.42 ~(((ord_less @ nat @ n @ (size_size @ list @ a @ xs)) => (((stream370371455e_snth @ a @ (stream1035003186_shift @ a @ xs @ s) @ n)) = ((nth @ a @ xs @ n)))) & (~(ord_less @ nat @ n @ (size_size @ list @ a @ xs)) => (((stream370371455e_snth @ a @ (stream1035003186_shift @ a @ xs @ s) @ n)) = ((stream370371455e_snth @ a @ s @ (minus_minus @ nat @ n @ (size_size @ list @ a @ xs)))))))),
% 0.61/0.42 inference(rectify,[],[f276])).
% 0.61/0.42 thf(f781,plain,(
% 0.61/0.42 ~(((((ord_less @ nat @ n @ (size_size @ list @ a @ xs))) = $true) => (((stream370371455e_snth @ a @ (stream1035003186_shift @ a @ xs @ s) @ n)) = ((nth @ a @ xs @ n)))) & (~ (((ord_less @ nat @ n @ (size_size @ list @ a @ xs))) = $true) => (((stream370371455e_snth @ a @ (stream1035003186_shift @ a @ xs @ s) @ n)) = ((stream370371455e_snth @ a @ s @ (minus_minus @ nat @ n @ (size_size @ list @ a @ xs)))))))),
% 0.61/0.42 inference(fool_elimination,[],[f780])).
% 0.61/0.42 thf(f790,plain,(
% 0.61/0.42 ~(((((ord_less @ nat @ n @ (size_size @ list @ a @ xs))) = $true) => (((stream370371455e_snth @ a @ (stream1035003186_shift @ a @ xs @ s) @ n)) = ((nth @ a @ xs @ n)))) & ((((ord_less @ nat @ n @ (size_size @ list @ a @ xs))) != $true) => (((stream370371455e_snth @ a @ (stream1035003186_shift @ a @ xs @ s) @ n)) = ((stream370371455e_snth @ a @ s @ (minus_minus @ nat @ n @ (size_size @ list @ a @ xs)))))))),
% 0.61/0.42 inference(flattening,[],[f781])).
% 0.61/0.42 thf(f815,plain,(
% 0.61/0.42 ((((stream370371455e_snth @ a @ (stream1035003186_shift @ a @ xs @ s) @ n)) != ((stream370371455e_snth @ a @ s @ (minus_minus @ nat @ n @ (size_size @ list @ a @ xs))))) & (((ord_less @ nat @ n @ (size_size @ list @ a @ xs))) != $true)) | ((((ord_less @ nat @ n @ (size_size @ list @ a @ xs))) = $true) & (((stream370371455e_snth @ a @ (stream1035003186_shift @ a @ xs @ s) @ n)) != ((nth @ a @ xs @ n))))),
% 0.61/0.42 inference(ennf_transformation,[],[f790])).
% 0.61/0.42 thf(f837,plain,(
% 0.61/0.42 ! [X1 : nat,X0 : nat] : (((((ord_less @ nat @ X1 @ X0)) = $true) | (X0 = X1)) | (((ord_less_eq @ nat @ X1 @ X0)) != $true))),
% 0.61/0.42 inference(ennf_transformation,[],[f659])).
% 0.61/0.42 thf(f838,plain,(
% 0.61/0.42 ! [X0 : nat,X1 : nat] : ((((ord_less @ nat @ X1 @ X0)) = $true) | (X0 = X1) | (((ord_less_eq @ nat @ X1 @ X0)) != $true))),
% 0.61/0.42 inference(flattening,[],[f837])).
% 0.61/0.42 thf(f840,plain,(
% 0.61/0.42 ! [X0 : $tType,X3 : nat,X1 : list @ X0,X2 : stream170649215stream @ X0] : ((((nth @ X0 @ X1 @ X3)) = ((stream370371455e_snth @ X0 @ (stream1035003186_shift @ X0 @ X1 @ X2) @ X3))) | (((ord_less @ nat @ X3 @ (size_size @ list @ X0 @ X1))) != $true))),
% 0.61/0.42 inference(ennf_transformation,[],[f591])).
% 0.61/0.42 thf(f854,plain,(
% 0.61/0.42 ! [X0 : $tType,X3 : list @ X0,X1 : stream170649215stream @ X0,X2 : nat] : ((((ord_less_eq @ nat @ (size_size @ list @ X0 @ X3) @ X2)) != $true) | (((stream370371455e_snth @ X0 @ X1 @ (minus_minus @ nat @ X2 @ (size_size @ list @ X0 @ X3)))) = ((stream370371455e_snth @ X0 @ (stream1035003186_shift @ X0 @ X3 @ X1) @ X2))))),
% 0.61/0.42 inference(ennf_transformation,[],[f325])).
% 0.61/0.42 thf(f897,plain,(
% 0.61/0.42 ! [X0 : $tType,X1 : nat,X2 : list @ X0,X3 : stream170649215stream @ X0] : ((((stream370371455e_snth @ X0 @ (stream1035003186_shift @ X0 @ X2 @ X3) @ X1)) = ((nth @ X0 @ X2 @ X1))) | (((ord_less @ nat @ X1 @ (size_size @ list @ X0 @ X2))) != $true))),
% 0.61/0.42 inference(rectify,[],[f840])).
% 0.61/0.42 thf(f898,plain,(
% 0.61/0.42 ! [X0 : $tType,X1 : list @ X0,X2 : stream170649215stream @ X0,X3 : nat] : ((((ord_less_eq @ nat @ (size_size @ list @ X0 @ X1) @ X3)) != $true) | (((stream370371455e_snth @ X0 @ (stream1035003186_shift @ X0 @ X1 @ X2) @ X3)) = ((stream370371455e_snth @ X0 @ X2 @ (minus_minus @ nat @ X3 @ (size_size @ list @ X0 @ X1))))))),
% 0.61/0.42 inference(rectify,[],[f854])).
% 0.61/0.42 thf(f904,plain,(
% 0.61/0.42 ( ! [X0 : nat,X1 : nat] : ((((ord_less_eq @ nat @ X1 @ X0)) = $true) | (((ord_less_eq @ nat @ X0 @ X1)) = $true)) )),
% 0.61/0.42 inference(cnf_transformation,[],[f469])).
% 0.61/0.42 thf(f925,plain,(
% 0.61/0.42 ( ! [X0 : nat] : ((((ord_less_eq @ nat @ X0 @ X0)) = $true)) )),
% 0.61/0.42 inference(cnf_transformation,[],[f485])).
% 0.61/0.42 thf(f958,plain,(
% 0.61/0.42 ( ! [X0 : $tType,X2 : list @ X0,X3 : stream170649215stream @ X0,X1 : nat] : ((((stream370371455e_snth @ X0 @ (stream1035003186_shift @ X0 @ X2 @ X3) @ X1)) = ((nth @ X0 @ X2 @ X1))) | (((ord_less @ nat @ X1 @ (size_size @ list @ X0 @ X2))) != $true)) )),
% 0.61/0.42 inference(cnf_transformation,[],[f897])).
% 0.61/0.42 thf(f959,plain,(
% 0.61/0.42 ( ! [X0 : $tType,X2 : stream170649215stream @ X0,X3 : nat,X1 : list @ X0] : ((((stream370371455e_snth @ X0 @ (stream1035003186_shift @ X0 @ X1 @ X2) @ X3)) = ((stream370371455e_snth @ X0 @ X2 @ (minus_minus @ nat @ X3 @ (size_size @ list @ X0 @ X1))))) | (((ord_less_eq @ nat @ (size_size @ list @ X0 @ X1) @ X3)) != $true)) )),
% 0.61/0.42 inference(cnf_transformation,[],[f898])).
% 0.61/0.42 thf(f963,plain,(
% 0.61/0.42 (((ord_less @ nat @ n @ (size_size @ list @ a @ xs))) != $true) | (((stream370371455e_snth @ a @ (stream1035003186_shift @ a @ xs @ s) @ n)) != ((nth @ a @ xs @ n)))),
% 0.61/0.42 inference(cnf_transformation,[],[f815])).
% 0.61/0.42 thf(f966,plain,(
% 0.61/0.42 (((stream370371455e_snth @ a @ (stream1035003186_shift @ a @ xs @ s) @ n)) != ((stream370371455e_snth @ a @ s @ (minus_minus @ nat @ n @ (size_size @ list @ a @ xs))))) | (((ord_less @ nat @ n @ (size_size @ list @ a @ xs))) = $true)),
% 0.61/0.42 inference(cnf_transformation,[],[f815])).
% 0.61/0.42 thf(f970,plain,(
% 0.61/0.42 ( ! [X0 : nat,X1 : nat] : ((((ord_less @ nat @ X1 @ X0)) = $true) | (X0 = X1) | (((ord_less_eq @ nat @ X1 @ X0)) != $true)) )),
% 0.61/0.42 inference(cnf_transformation,[],[f838])).
% 0.61/0.42 thf(f972,definition,(
% 0.61/0.42 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.61/0.42 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.61/0.42 thf(f979,definition,(
% 0.61/0.42 spl17_1 <=> (((stream370371455e_snth @ a @ (stream1035003186_shift @ a @ xs @ s) @ n)) = ((stream370371455e_snth @ a @ s @ (minus_minus @ nat @ n @ (size_size @ list @ a @ xs)))))),
% 0.61/0.42 introduced(definition,[new_symbols(definition,[spl17_1])],[avatar_definition])).
% 0.61/0.42 thf(f981,plain,(
% 0.61/0.42 (((stream370371455e_snth @ a @ (stream1035003186_shift @ a @ xs @ s) @ n)) != ((stream370371455e_snth @ a @ s @ (minus_minus @ nat @ n @ (size_size @ list @ a @ xs))))) | spl17_1),
% 0.61/0.42 inference(avatar_component_clause,[],[f979])).
% 0.61/0.42 thf(f983,definition,(
% 0.61/0.42 spl17_2 <=> (((ord_less @ nat @ n @ (size_size @ list @ a @ xs))) = $true)),
% 0.61/0.42 introduced(definition,[new_symbols(definition,[spl17_2])],[avatar_definition])).
% 0.61/0.42 thf(f984,plain,(
% 0.61/0.42 (((ord_less @ nat @ n @ (size_size @ list @ a @ xs))) != $true) | spl17_2),
% 0.61/0.42 inference(avatar_component_clause,[],[f983])).
% 0.61/0.42 thf(f986,plain,(
% 0.61/0.42 ~spl17_1 | spl17_2),
% 0.61/0.42 inference(avatar_split_clause,[],[f966,f983,f979])).
% 0.61/0.42 thf(f987,plain,(
% 0.61/0.42 (((ord_less @ nat @ n @ (size_size @ list @ a @ xs))) != $true)),
% 0.61/0.42 inference(forward_subsumption_resolution,[],[f963,f958])).
% 0.61/0.42 thf(f993,plain,(
% 0.61/0.42 ~spl17_2),
% 0.61/0.42 inference(avatar_split_clause,[],[f987,f983])).
% 0.61/0.42 thf(f996,plain,(
% 0.61/0.42 (((ord_less @ nat @ n @ (size_size @ list @ a @ xs))) = $false) | ($true != $true) | spl17_2),
% 0.61/0.42 inference(superposition,[],[f984,f972])).
% 0.61/0.42 thf(f997,plain,(
% 0.61/0.42 (((ord_less @ nat @ n @ (size_size @ list @ a @ xs))) = $false) | spl17_2),
% 0.61/0.42 inference(trivial_inequality_removal,[],[f996])).
% 0.61/0.42 thf(f1005,definition,(
% 0.61/0.42 spl17_5 <=> (n = ((size_size @ list @ a @ xs)))),
% 0.61/0.42 introduced(definition,[new_symbols(definition,[spl17_5])],[avatar_definition])).
% 0.61/0.42 thf(f1007,plain,(
% 0.61/0.42 (n = ((size_size @ list @ a @ xs))) | ~spl17_5),
% 0.61/0.42 inference(avatar_component_clause,[],[f1005])).
% 0.61/0.42 thf(f1010,definition,(
% 0.61/0.42 spl17_6 <=> (((ord_less_eq @ nat @ n @ (size_size @ list @ a @ xs))) = $true)),
% 0.61/0.42 introduced(definition,[new_symbols(definition,[spl17_6])],[avatar_definition])).
% 0.61/0.42 thf(f1012,plain,(
% 0.61/0.42 (((ord_less_eq @ nat @ n @ (size_size @ list @ a @ xs))) != $true) | spl17_6),
% 0.61/0.42 inference(avatar_component_clause,[],[f1010])).
% 0.61/0.42 thf(f1015,plain,(
% 0.61/0.42 (((stream370371455e_snth @ a @ s @ (minus_minus @ nat @ n @ (size_size @ list @ a @ xs)))) != ((stream370371455e_snth @ a @ s @ (minus_minus @ nat @ n @ (size_size @ list @ a @ xs))))) | (((ord_less_eq @ nat @ (size_size @ list @ a @ xs) @ n)) != $true) | spl17_1),
% 0.61/0.42 inference(superposition,[],[f981,f959])).
% 0.61/0.42 thf(f1016,plain,(
% 0.61/0.42 (((ord_less_eq @ nat @ (size_size @ list @ a @ xs) @ n)) != $true) | spl17_1),
% 0.61/0.42 inference(trivial_inequality_removal,[],[f1015])).
% 0.61/0.42 thf(f1018,plain,(
% 0.61/0.42 (n = ((size_size @ list @ a @ xs))) | ($false = $true) | (((ord_less_eq @ nat @ n @ (size_size @ list @ a @ xs))) != $true) | spl17_2),
% 0.61/0.42 inference(superposition,[],[f997,f970])).
% 0.61/0.42 thf(f1024,plain,(
% 0.61/0.42 (((ord_less_eq @ nat @ n @ (size_size @ list @ a @ xs))) != $true) | (n = ((size_size @ list @ a @ xs))) | spl17_2),
% 0.61/0.42 inference(trivial_inequality_removal,[],[f1018])).
% 0.61/0.42 thf(f1029,plain,(
% 0.61/0.42 (((ord_less_eq @ nat @ (size_size @ list @ a @ xs) @ n)) = $true) | ($true != $true) | spl17_6),
% 0.61/0.42 inference(superposition,[],[f1012,f904])).
% 0.61/0.42 thf(f1037,plain,(
% 0.61/0.42 (((ord_less_eq @ nat @ (size_size @ list @ a @ xs) @ n)) = $true) | spl17_6),
% 0.61/0.42 inference(trivial_inequality_removal,[],[f1029])).
% 0.61/0.42 thf(f1038,plain,(
% 0.61/0.42 $false | (spl17_1 | spl17_6)),
% 0.61/0.42 inference(forward_subsumption_resolution,[],[f1037,f1016])).
% 0.61/0.42 thf(f1039,plain,(
% 0.61/0.42 spl17_1 | spl17_6),
% 0.61/0.42 inference(avatar_contradiction_clause,[],[f1038])).
% 0.61/0.42 thf(f1040,plain,(
% 0.61/0.42 spl17_5 | ~spl17_6 | spl17_2),
% 0.61/0.42 inference(avatar_split_clause,[],[f1024,f983,f1010,f1005])).
% 0.61/0.42 thf(f1069,plain,(
% 0.61/0.42 ($true != $true) | (((ord_less_eq @ nat @ (size_size @ list @ a @ xs) @ n)) = $false) | spl17_1),
% 0.61/0.42 inference(superposition,[],[f1016,f972])).
% 0.61/0.42 thf(f1071,plain,(
% 0.61/0.42 (((ord_less_eq @ nat @ (size_size @ list @ a @ xs) @ n)) = $false) | spl17_1),
% 0.61/0.42 inference(trivial_inequality_removal,[],[f1069])).
% 0.61/0.42 thf(f1079,plain,(
% 0.61/0.42 ($false = ((ord_less_eq @ nat @ n @ n))) | (spl17_1 | ~spl17_5)),
% 0.61/0.42 inference(forward_demodulation,[],[f1071,f1007])).
% 0.61/0.42 thf(f1084,plain,(
% 0.61/0.42 ($false = $true) | (spl17_1 | ~spl17_5)),
% 0.61/0.42 inference(forward_demodulation,[],[f1079,f925])).
% 0.61/0.42 thf(f1085,plain,(
% 0.61/0.42 $false | (spl17_1 | ~spl17_5)),
% 0.61/0.42 inference(trivial_inequality_removal,[],[f1084])).
% 0.61/0.42 thf(f1086,plain,(
% 0.61/0.42 spl17_1 | ~spl17_5),
% 0.61/0.42 inference(avatar_contradiction_clause,[],[f1085])).
% 0.61/0.42 cnf(s1, plain, ~spl17_1 | spl17_2, inference(sat_conversion,[],[f986])).
% 0.61/0.42 cnf(s3, plain, ~spl17_2, inference(sat_conversion,[],[f993])).
% 0.61/0.42 cnf(s6, plain, spl17_1 | spl17_6, inference(sat_conversion,[],[f1039])).
% 0.61/0.42 cnf(s7, plain, spl17_2 | spl17_5 | ~spl17_6, inference(sat_conversion,[],[f1040])).
% 0.61/0.42 cnf(s10, plain, spl17_1 | ~spl17_5, inference(sat_conversion,[],[f1086])).
% 0.61/0.42 cnf(s11, plain, ~spl17_1, inference(rat,[],[s1,s3])).
% 0.61/0.42 cnf(s12, plain, ~spl17_5, inference(rat,[],[s10,s11])).
% 0.61/0.42 cnf(s13, plain, spl17_6, inference(rat,[],[s6,s11])).
% 0.61/0.42 cnf(s14, plain, $false, inference(rat,[],[s7,s3,s13,s12])).
% 0.61/0.42 thf(f1089,plain,(
% 0.61/0.42 $false),
% 0.61/0.42 inference(avatar_sat_refutation,[],[s14])).
% 0.61/0.42 % SZS output end Proof for theBenchmark
% 0.61/0.42 % (1647443)------------------------------
% 0.61/0.42 % (1647443)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (1647443)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (1647443)CaDiCaL version: 2.1.3
% 0.61/0.42 % (1647443)Termination reason: Refutation
% 0.61/0.42 % (1647443)Time elapsed: 0.016 s
% 0.61/0.42 % (1647443)Peak memory usage: 14 MB
% 0.61/0.42 % (1647443)Instructions burned: 60 (million)
% 0.61/0.42 % (1647410)Success in time 0.138 s
% 0.61/0.42 % Vampire exiting
%------------------------------------------------------------------------------