%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV481^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 08:38:43 AM UTC 2026
% Result : Theorem 0.20s 0.30s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV481^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n018.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 15:55:26 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.29 % (258298)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.29 % (258307)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3410972510:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.29 % (258309)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.29 % (258309)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
% 0.20/0.29 % (258303)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3340536999:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.29 % (258304)lrs+10_16_si=on:nwc=1.5:random_seed=1262176649:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.29 % (258305)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=309357329:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.29 % (258307)Instruction limit reached!
% 0.20/0.29 % (258307)------------------------------
% 0.20/0.29 % (258307)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (258307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (258308)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2649458485:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.29 % (258307)CaDiCaL version: 2.1.3
% 0.20/0.29 % (258307)Termination reason: Instruction limit
% 0.20/0.29 % (258307)Termination phase: Saturation
% 0.20/0.29 % (258307)Time elapsed: 0.008 s
% 0.20/0.29 % (258306)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=3367262581: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)
% 0.20/0.29 % (258307)Peak memory usage: 12 MB
% 0.20/0.29 % (258307)Instructions burned: 26 (million)
% 0.20/0.29 % (258309)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=3802597760:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.30 % (258305)Instruction limit reached!
% 0.20/0.30 % (258305)------------------------------
% 0.20/0.30 % (258305)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (258305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (258305)CaDiCaL version: 2.1.3
% 0.20/0.30 % (258305)Termination reason: Instruction limit
% 0.20/0.30 % (258305)Termination phase: Saturation
% 0.20/0.30 % (258305)Time elapsed: 0.003 s
% 0.20/0.30 % (258305)Peak memory usage: 12 MB
% 0.20/0.30 % (258305)Instructions burned: 4 (million)
% 0.20/0.30 % (258306)Refutation not found, incomplete strategy
% 0.20/0.30 % (258306)------------------------------
% 0.20/0.30 % (258306)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (258306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (258306)CaDiCaL version: 2.1.3
% 0.20/0.30 % (258306)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.30 % (258306)Time elapsed: 0.003 s
% 0.20/0.30 % (258306)Peak memory usage: 12 MB
% 0.20/0.30 % (258306)Instructions burned: 4 (million)
% 0.20/0.30 % (258306)------------------------------
% 0.20/0.30 % (258306)------------------------------
% 0.20/0.30 % (258309)Refutation not found, incomplete strategy
% 0.20/0.30 % (258309)------------------------------
% 0.20/0.30 % (258309)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (258309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (258309)CaDiCaL version: 2.1.3
% 0.20/0.30 % (258309)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.30 % (258309)Time elapsed: 0.004 s
% 0.20/0.30 % (258309)Peak memory usage: 12 MB
% 0.20/0.30 % (258309)Instructions burned: 6 (million)
% 0.20/0.30 % (258309)------------------------------
% 0.20/0.30 % (258309)------------------------------
% 0.20/0.30 % (258304)Instruction limit reached!
% 0.20/0.30 % (258304)------------------------------
% 0.20/0.30 % (258304)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (258304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (258304)CaDiCaL version: 2.1.3
% 0.20/0.30 % (258304)Termination reason: Instruction limit
% 0.20/0.30 % (258304)Termination phase: Saturation
% 0.20/0.30 % (258304)Time elapsed: 0.011 s
% 0.20/0.30 % (258304)Peak memory usage: 12 MB
% 0.20/0.30 % (258304)Instructions burned: 19 (million)
% 0.20/0.30 % (258319)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.30 % (258319)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3638529578:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.20/0.30 % (258319)Instruction limit reached!
% 0.20/0.30 % (258319)------------------------------
% 0.20/0.30 % (258319)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (258319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (258319)CaDiCaL version: 2.1.3
% 0.20/0.30 % (258319)Termination reason: Instruction limit
% 0.20/0.30 % (258319)Termination phase: Saturation
% 0.20/0.30 % (258319)Time elapsed: 0.003 s
% 0.20/0.30 % (258319)Peak memory usage: 12 MB
% 0.20/0.30 % (258319)Instructions burned: 10 (million)
% 0.20/0.30 % (258317)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2983914892:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.30 % (258318)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2416131278:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.20/0.30 % (258317)Instruction limit reached!
% 0.20/0.30 % (258317)------------------------------
% 0.20/0.30 % (258317)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (258317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (258317)CaDiCaL version: 2.1.3
% 0.20/0.30 % (258317)Termination reason: Instruction limit
% 0.20/0.30 % (258317)Termination phase: Saturation
% 0.20/0.30 % (258317)Time elapsed: 0.002 s
% 0.20/0.30 % (258317)Peak memory usage: 12 MB
% 0.20/0.30 % (258317)Instructions burned: 2 (million)
% 0.20/0.30 % (258320)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2880946644:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.20/0.30 % (258321)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
% 0.20/0.30 % (258321)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.30 % (258318)Instruction limit reached!
% 0.20/0.30 % (258318)------------------------------
% 0.20/0.30 % (258318)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (258318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (258318)CaDiCaL version: 2.1.3
% 0.20/0.30 % (258318)Termination reason: Instruction limit
% 0.20/0.30 % (258318)Termination phase: Saturation
% 0.20/0.30 % (258318)Time elapsed: 0.004 s
% 0.20/0.30 % (258318)Peak memory usage: 12 MB
% 0.20/0.30 % (258318)Instructions burned: 6 (million)
% 0.20/0.30 % (258323)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=3239924989:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.20/0.30 % (258321)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3568990081:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.20/0.30 % (258320) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-258298-258320"...
% 0.20/0.30 % (258320)...printing done.
% 0.20/0.30 % (258321)Refutation not found, incomplete strategy
% 0.20/0.30 % (258321)------------------------------
% 0.20/0.30 % (258321)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (258321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (258321)CaDiCaL version: 2.1.3
% 0.20/0.30 % (258321)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.30 % (258321)Time elapsed: 0.005 s
% 0.20/0.30 % (258321)Peak memory usage: 12 MB
% 0.20/0.30 % (258321)Instructions burned: 9 (million)
% 0.20/0.30 % (258320)Refutation found. Thanks to Tanya!
% 0.20/0.30 % SZS status Theorem for theBenchmark
% 0.20/0.30 % SZS output start Proof for theBenchmark
% 0.20/0.30 thf(type_def_5, type, 'type/pair/prod': ($tType * $tType) > $tType).
% 0.20/0.30 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.30 thf(type_def_7, type, sK0: $tType).
% 0.20/0.30 thf(type_def_8, type, sK1: $tType).
% 0.20/0.30 thf(func_def_0, type, 'const/sets/SETSPEC': !>[X0: $tType]:((X0 > $o > X0 > $o))).
% 0.20/0.30 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.20/0.30 thf(func_def_2, type, 'const/sets/GSPEC': !>[X0: $tType]:(((X0 > $o) > X0 > $o))).
% 0.20/0.30 thf(func_def_3, type, 'const/sets/FINITE': !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.30 thf(func_def_4, type, 'const/pair/,': !>[X0: $tType, X1: $tType]:((X0 > X1 > 'type/pair/prod' @ X0 @ X1))).
% 0.20/0.30 thf(func_def_8, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.30 thf(func_def_9, type, db2: !>[X0: $tType]:(X0)).
% 0.20/0.30 thf(func_def_10, type, vAND: ($o > $o > $o)).
% 0.20/0.30 thf(func_def_11, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.30 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.30 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.30 thf(func_def_14, type, sK2: (sK0 > $o)).
% 0.20/0.30 thf(func_def_15, type, sK3: (sK1 > $o)).
% 0.20/0.30 thf(func_def_16, type, sK4: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > (X0 > $o) > X0))).
% 0.20/0.30 thf(func_def_17, type, vNOT: ($o > $o)).
% 0.20/0.30 thf(f1,axiom,(
% 0.20/0.30 ! [X2 : $tType,X0 : $tType,X1 : $tType,X5 : (X0 > X1 > $o),X3 : (X0 > X1 > X2),X4 : (X0 > $o)] : ((! [X6 : X0] : (('const/sets/IN' @ X0 @ X6 @ X4) => ('const/sets/FINITE' @ X1 @ (X5 @ X6))) & ('const/sets/FINITE' @ X0 @ X4)) => ('const/sets/FINITE' @ X2 @ ('const/sets/GSPEC' @ X2 @ (^[X6 : X2] : (? [X8 : X1,X7 : X0] : ('const/sets/SETSPEC' @ X2 @ X6 @ ('const/sets/IN' @ X1 @ X8 @ (X5 @ X7)) & ('const/sets/IN' @ X0 @ X7 @ X4) @ (X3 @ X7 @ X8)))))))),
% 0.20/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/FINITE_PRODUCT_DEPENDENT_')).
% 0.20/0.30 thf(f2,conjecture,(
% 0.20/0.30 ! [X1 : $tType,X0 : $tType,X3 : (X1 > $o),X2 : (X0 > $o)] : ((('const/sets/FINITE' @ X0 @ X2) & ('const/sets/FINITE' @ X1 @ X3)) => ('const/sets/FINITE' @ 'type/pair/prod' @ X0 @ X1 @ ('const/sets/GSPEC' @ 'type/pair/prod' @ X0 @ X1 @ (^[X4 : 'type/pair/prod' @ X0 @ X1] : (? [X6 : X1,X5 : X0] : ('const/sets/SETSPEC' @ 'type/pair/prod' @ X0 @ X1 @ X4 @ ('const/sets/IN' @ X1 @ X6 @ X3) & ('const/sets/IN' @ X0 @ X5 @ X2) @ ('const/pair/,' @ X0 @ X1 @ X5 @ X6)))))))),
% 0.20/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/FINITE_PRODUCT_')).
% 0.20/0.30 thf(f3,negated_conjecture,(
% 0.20/0.30 ~ ! [X1 : $tType,X0 : $tType,X3 : (X1 > $o),X2 : (X0 > $o)] : ((('const/sets/FINITE' @ X0 @ X2) & ('const/sets/FINITE' @ X1 @ X3)) => ('const/sets/FINITE' @ 'type/pair/prod' @ X0 @ X1 @ ('const/sets/GSPEC' @ 'type/pair/prod' @ X0 @ X1 @ (^[X4 : 'type/pair/prod' @ X0 @ X1] : (? [X6 : X1,X5 : X0] : ('const/sets/SETSPEC' @ 'type/pair/prod' @ X0 @ X1 @ X4 @ ('const/sets/IN' @ X1 @ X6 @ X3) & ('const/sets/IN' @ X0 @ X5 @ X2) @ ('const/pair/,' @ X0 @ X1 @ X5 @ X6)))))))),
% 0.20/0.30 inference(negated_conjecture,[status(cth)],[f2])).
% 0.20/0.30 thf(f4,plain,(
% 0.20/0.30 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : (X1 > X2 > $o),X4 : (X1 > X2 > X0),X5 : (X1 > $o)] : ((! [X6 : X1] : (('const/sets/IN' @ X1 @ X6 @ X5) => ('const/sets/FINITE' @ X2 @ (X3 @ X6))) & ('const/sets/FINITE' @ X1 @ X5)) => ('const/sets/FINITE' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[X7 : X0] : (? [X8 : X2,X9 : X1] : ('const/sets/SETSPEC' @ X0 @ X7 @ ('const/sets/IN' @ X2 @ X8 @ (X3 @ X9)) & ('const/sets/IN' @ X1 @ X9 @ X5) @ (X4 @ X9 @ X8)))))))),
% 0.20/0.30 inference(rectify,[],[f1])).
% 0.20/0.30 thf(f5,plain,(
% 0.20/0.30 ! [X2 : $tType,X1 : $tType,X0 : $tType,X3 : (X1 > X2 > $o),X4 : (X1 > X2 > X0),X5 : (X1 > $o)] : ((! [X6 : X1] : (($true = (('const/sets/IN' @ X1 @ X6 @ X5))) => ($true = (('const/sets/FINITE' @ X2 @ (X3 @ X6))))) & ($true = (('const/sets/FINITE' @ X1 @ X5)))) => ($true = (('const/sets/FINITE' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X1 @ (^[Y1 : X1]: (?? @ X2 @ (^[Y2 : X2]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X1 @ Y1 @ X5) & ('const/sets/IN' @ X2 @ Y2 @ (X3 @ Y1))) @ (X4 @ Y1 @ Y2))))))))))))),
% 0.20/0.30 inference(fool_elimination,[],[f4])).
% 0.20/0.30 thf(f6,plain,(
% 0.20/0.30 ~ ! [X0 : $tType,X1 : $tType,X2 : (X0 > $o),X3 : (X1 > $o)] : ((('const/sets/FINITE' @ X1 @ X3) & ('const/sets/FINITE' @ X0 @ X2)) => ('const/sets/FINITE' @ 'type/pair/prod' @ X1 @ X0 @ ('const/sets/GSPEC' @ 'type/pair/prod' @ X1 @ X0 @ (^[X4 : 'type/pair/prod' @ X1 @ X0] : (? [X5 : X0,X6 : X1] : ('const/sets/SETSPEC' @ 'type/pair/prod' @ X1 @ X0 @ X4 @ ('const/sets/IN' @ X0 @ X5 @ X2) & ('const/sets/IN' @ X1 @ X6 @ X3) @ ('const/pair/,' @ X1 @ X0 @ X6 @ X5)))))))),
% 0.20/0.30 inference(rectify,[],[f3])).
% 0.20/0.30 thf(f7,plain,(
% 0.20/0.30 ~ ! [X0 : $tType,X1 : $tType,X3 : (X1 > $o),X2 : (X0 > $o)] : ((((('const/sets/FINITE' @ X1 @ X3)) = $true) & ((('const/sets/FINITE' @ X0 @ X2)) = $true)) => ($true = (('const/sets/FINITE' @ 'type/pair/prod' @ X1 @ X0 @ ('const/sets/GSPEC' @ 'type/pair/prod' @ X1 @ X0 @ (^[Y0 : 'type/pair/prod' @ X1 @ X0]: (?? @ X1 @ (^[Y1 : X1]: (?? @ X0 @ (^[Y2 : X0]: ('const/sets/SETSPEC' @ 'type/pair/prod' @ X1 @ X0 @ Y0 @ (('const/sets/IN' @ X1 @ Y1 @ X3) & ('const/sets/IN' @ X0 @ Y2 @ X2)) @ ('const/pair/,' @ X1 @ X0 @ Y1 @ Y2))))))))))))),
% 0.20/0.30 inference(fool_elimination,[],[f6])).
% 0.20/0.30 thf(f8,plain,(
% 0.20/0.30 ? [X0 : $tType,X1 : $tType,X3 : (X1 > $o),X2 : (X0 > $o)] : (($true != (('const/sets/FINITE' @ 'type/pair/prod' @ X1 @ X0 @ ('const/sets/GSPEC' @ 'type/pair/prod' @ X1 @ X0 @ (^[Y0 : 'type/pair/prod' @ X1 @ X0]: (?? @ X1 @ (^[Y1 : X1]: (?? @ X0 @ (^[Y2 : X0]: ('const/sets/SETSPEC' @ 'type/pair/prod' @ X1 @ X0 @ Y0 @ (('const/sets/IN' @ X1 @ Y1 @ X3) & ('const/sets/IN' @ X0 @ Y2 @ X2)) @ ('const/pair/,' @ X1 @ X0 @ Y1 @ Y2))))))))))) & (((('const/sets/FINITE' @ X1 @ X3)) = $true) & ((('const/sets/FINITE' @ X0 @ X2)) = $true)))),
% 0.20/0.30 inference(ennf_transformation,[],[f7])).
% 0.20/0.30 thf(f9,plain,(
% 0.20/0.30 ? [X0 : $tType,X1 : $tType,X2 : (X0 > $o),X3 : (X1 > $o)] : (($true != (('const/sets/FINITE' @ 'type/pair/prod' @ X1 @ X0 @ ('const/sets/GSPEC' @ 'type/pair/prod' @ X1 @ X0 @ (^[Y0 : 'type/pair/prod' @ X1 @ X0]: (?? @ X1 @ (^[Y1 : X1]: (?? @ X0 @ (^[Y2 : X0]: ('const/sets/SETSPEC' @ 'type/pair/prod' @ X1 @ X0 @ Y0 @ (('const/sets/IN' @ X1 @ Y1 @ X3) & ('const/sets/IN' @ X0 @ Y2 @ X2)) @ ('const/pair/,' @ X1 @ X0 @ Y1 @ Y2))))))))))) & ((('const/sets/FINITE' @ X1 @ X3)) = $true) & ((('const/sets/FINITE' @ X0 @ X2)) = $true))),
% 0.20/0.30 inference(flattening,[],[f8])).
% 0.20/0.30 thf(f10,plain,(
% 0.20/0.30 ! [X2 : $tType,X1 : $tType,X0 : $tType,X3 : (X1 > X2 > $o),X4 : (X1 > X2 > X0),X5 : (X1 > $o)] : (($true = (('const/sets/FINITE' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X1 @ (^[Y1 : X1]: (?? @ X2 @ (^[Y2 : X2]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X1 @ Y1 @ X5) & ('const/sets/IN' @ X2 @ Y2 @ (X3 @ Y1))) @ (X4 @ Y1 @ Y2))))))))))) | (? [X6 : X1] : (($true = (('const/sets/IN' @ X1 @ X6 @ X5))) & ($true != (('const/sets/FINITE' @ X2 @ (X3 @ X6))))) | ($true != (('const/sets/FINITE' @ X1 @ X5)))))),
% 0.20/0.30 inference(ennf_transformation,[],[f5])).
% 0.20/0.30 thf(f11,plain,(
% 0.20/0.30 ! [X0 : $tType,X1 : $tType,X2 : $tType,X5 : (X1 > $o),X3 : (X1 > X2 > $o),X4 : (X1 > X2 > X0)] : (($true != (('const/sets/FINITE' @ X1 @ X5))) | ? [X6 : X1] : (($true = (('const/sets/IN' @ X1 @ X6 @ X5))) & ($true != (('const/sets/FINITE' @ X2 @ (X3 @ X6))))) | ($true = (('const/sets/FINITE' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X1 @ (^[Y1 : X1]: (?? @ X2 @ (^[Y2 : X2]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X1 @ Y1 @ X5) & ('const/sets/IN' @ X2 @ Y2 @ (X3 @ Y1))) @ (X4 @ Y1 @ Y2))))))))))))),
% 0.20/0.30 inference(flattening,[],[f10])).
% 0.20/0.30 thf(f12,plain,(
% 0.20/0.30 ($true != (('const/sets/FINITE' @ 'type/pair/prod' @ sK1 @ sK0 @ ('const/sets/GSPEC' @ 'type/pair/prod' @ sK1 @ sK0 @ (^[Y0 : 'type/pair/prod' @ sK1 @ sK0]: (?? @ sK1 @ (^[Y1 : sK1]: (?? @ sK0 @ (^[Y2 : sK0]: ('const/sets/SETSPEC' @ 'type/pair/prod' @ sK1 @ sK0 @ Y0 @ (('const/sets/IN' @ sK1 @ Y1 @ sK3) & ('const/sets/IN' @ sK0 @ Y2 @ sK2)) @ ('const/pair/,' @ sK1 @ sK0 @ Y1 @ Y2))))))))))) & ($true = (('const/sets/FINITE' @ sK1 @ sK3))) & ($true = (('const/sets/FINITE' @ sK0 @ sK2)))),
% 0.20/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f9])).
% 0.20/0.30 thf(f13,plain,(
% 0.20/0.30 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : (X1 > $o),X4 : (X1 > X2 > $o),X5 : (X1 > X2 > X0)] : (((('const/sets/FINITE' @ X1 @ X3)) != $true) | ? [X6 : X1] : (((('const/sets/IN' @ X1 @ X6 @ X3)) = $true) & ($true != (('const/sets/FINITE' @ X2 @ (X4 @ X6))))) | ($true = (('const/sets/FINITE' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X1 @ (^[Y1 : X1]: (?? @ X2 @ (^[Y2 : X2]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X1 @ Y1 @ X3) & ('const/sets/IN' @ X2 @ Y2 @ (X4 @ Y1))) @ (X5 @ Y1 @ Y2))))))))))))),
% 0.20/0.30 inference(rectify,[],[f11])).
% 0.20/0.30 thf(f14,plain,(
% 0.20/0.30 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : (X1 > $o),X4 : (X1 > X2 > $o),X5 : (X1 > X2 > X0)] : (((('const/sets/FINITE' @ X1 @ X3)) != $true) | (($true = (('const/sets/IN' @ X1 @ (sK4 @ X1 @ X2 @ X4 @ X3) @ X3))) & ($true != (('const/sets/FINITE' @ X2 @ (X4 @ (sK4 @ X1 @ X2 @ X4 @ X3)))))) | ($true = (('const/sets/FINITE' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X1 @ (^[Y1 : X1]: (?? @ X2 @ (^[Y2 : X2]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X1 @ Y1 @ X3) & ('const/sets/IN' @ X2 @ Y2 @ (X4 @ Y1))) @ (X5 @ Y1 @ Y2))))))))))))),
% 0.20/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X6,sK4 @ X1 @ X2 @ X4 @ X3)],[f13])).
% 0.20/0.30 thf(f15,plain,(
% 0.20/0.30 ($true = (('const/sets/FINITE' @ sK0 @ sK2)))),
% 0.20/0.30 inference(cnf_transformation,[],[f12])).
% 0.20/0.30 thf(f16,plain,(
% 0.20/0.30 ($true = (('const/sets/FINITE' @ sK1 @ sK3)))),
% 0.20/0.30 inference(cnf_transformation,[],[f12])).
% 0.20/0.30 thf(f17,plain,(
% 0.20/0.30 ($true != (('const/sets/FINITE' @ 'type/pair/prod' @ sK1 @ sK0 @ ('const/sets/GSPEC' @ 'type/pair/prod' @ sK1 @ sK0 @ (^[Y0 : 'type/pair/prod' @ sK1 @ sK0]: (?? @ sK1 @ (^[Y1 : sK1]: (?? @ sK0 @ (^[Y2 : sK0]: ('const/sets/SETSPEC' @ 'type/pair/prod' @ sK1 @ sK0 @ Y0 @ (('const/sets/IN' @ sK1 @ Y1 @ sK3) & ('const/sets/IN' @ sK0 @ Y2 @ sK2)) @ ('const/pair/,' @ sK1 @ sK0 @ Y1 @ Y2)))))))))))),
% 0.20/0.30 inference(cnf_transformation,[],[f12])).
% 0.20/0.30 thf(f18,plain,(
% 0.20/0.30 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : (X1 > $o),X4 : (X1 > X2 > $o),X5 : (X1 > X2 > X0)] : (($true != (('const/sets/FINITE' @ X2 @ (X4 @ (sK4 @ X1 @ X2 @ X4 @ X3))))) | ((('const/sets/FINITE' @ X1 @ X3)) != $true) | ($true = (('const/sets/FINITE' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X1 @ (^[Y1 : X1]: (?? @ X2 @ (^[Y2 : X2]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X1 @ Y1 @ X3) & ('const/sets/IN' @ X2 @ Y2 @ (X4 @ Y1))) @ (X5 @ Y1 @ Y2)))))))))))) )),
% 0.20/0.30 inference(cnf_transformation,[],[f14])).
% 0.20/0.30 thf(f21,definition,(
% 0.20/0.30 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.20/0.30 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.20/0.30 thf(f22,plain,(
% 0.20/0.30 ( ! [X0 : $tType,X2 : $tType,X3 : (X0 > sK0 > X2),X1 : (X0 > $o)] : (($true != $true) | ($true = (('const/sets/FINITE' @ X2 @ ('const/sets/GSPEC' @ X2 @ (^[Y0 : X2]: (?? @ X0 @ (^[Y1 : X0]: (?? @ sK0 @ (^[Y2 : sK0]: ('const/sets/SETSPEC' @ X2 @ Y0 @ (('const/sets/IN' @ X0 @ Y1 @ X1) & ('const/sets/IN' @ sK0 @ Y2 @ ((^[Y3 : X0]: ((^[Y4 : sK0]: (sK2 @ ((^[Y5 : X0]: ((^[Y6 : sK0]: (Y6)))) @ Y3 @ Y4))))) @ Y1))) @ (X3 @ Y1 @ Y2))))))))))) | ($true != (('const/sets/FINITE' @ X0 @ X1)))) )),
% 0.20/0.30 inference(constrained_superposition,[],[f18,f15])).
% 0.20/0.30 thf(f24,plain,(
% 0.20/0.30 ( ! [X0 : $tType,X2 : $tType,X3 : (X0 > sK0 > X2),X1 : (X0 > $o)] : (($true != (('const/sets/FINITE' @ X0 @ X1))) | ($true = (('const/sets/FINITE' @ X2 @ ('const/sets/GSPEC' @ X2 @ (^[Y0 : X2]: (?? @ X0 @ (^[Y1 : X0]: (?? @ sK0 @ (^[Y2 : sK0]: ('const/sets/SETSPEC' @ X2 @ Y0 @ (('const/sets/IN' @ X0 @ Y1 @ X1) & ('const/sets/IN' @ sK0 @ Y2 @ ((^[Y3 : X0]: ((^[Y4 : sK0]: (sK2 @ ((^[Y5 : X0]: ((^[Y6 : sK0]: (Y6)))) @ Y3 @ Y4))))) @ Y1))) @ (X3 @ Y1 @ Y2)))))))))))) )),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f22])).
% 0.20/0.30 thf(f25,plain,(
% 0.20/0.30 ( ! [X0 : $tType,X2 : $tType,X3 : (X0 > sK0 > X2),X1 : (X0 > $o)] : (($true != (('const/sets/FINITE' @ X0 @ X1))) | ($true = (('const/sets/FINITE' @ X2 @ ('const/sets/GSPEC' @ X2 @ (^[Y0 : X2]: (?? @ X0 @ (^[Y1 : X0]: (?? @ sK0 @ (^[Y2 : sK0]: ('const/sets/SETSPEC' @ X2 @ Y0 @ (('const/sets/IN' @ X0 @ Y1 @ X1) & ('const/sets/IN' @ sK0 @ Y2 @ sK2)) @ (X3 @ Y1 @ Y2)))))))))))) )),
% 0.20/0.30 inference(beta-eta_normalization,[],[f24])).
% 0.20/0.30 thf(f29,plain,(
% 0.20/0.30 ($false = (('const/sets/FINITE' @ 'type/pair/prod' @ sK1 @ sK0 @ ('const/sets/GSPEC' @ 'type/pair/prod' @ sK1 @ sK0 @ (^[Y0 : 'type/pair/prod' @ sK1 @ sK0]: (?? @ sK1 @ (^[Y1 : sK1]: (?? @ sK0 @ (^[Y2 : sK0]: ('const/sets/SETSPEC' @ 'type/pair/prod' @ sK1 @ sK0 @ Y0 @ (('const/sets/IN' @ sK1 @ Y1 @ sK3) & ('const/sets/IN' @ sK0 @ Y2 @ sK2)) @ ('const/pair/,' @ sK1 @ sK0 @ Y1 @ Y2)))))))))))),
% 0.20/0.30 inference(unit_resulting_resolution,[],[f21,f17])).
% 0.20/0.30 thf(f53,plain,(
% 0.20/0.30 ( ! [X0 : $tType,X1 : (sK1 > sK0 > X0)] : (($true = (('const/sets/FINITE' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ sK1 @ (^[Y1 : sK1]: (?? @ sK0 @ (^[Y2 : sK0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ sK1 @ Y1 @ sK3) & ('const/sets/IN' @ sK0 @ Y2 @ sK2)) @ (X1 @ Y1 @ Y2))))))))))) | ($true != $true)) )),
% 0.20/0.30 inference(constrained_superposition,[],[f25,f16])).
% 0.20/0.30 thf(f55,plain,(
% 0.20/0.30 ( ! [X0 : $tType,X1 : (sK1 > sK0 > X0)] : (($true = (('const/sets/FINITE' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ sK1 @ (^[Y1 : sK1]: (?? @ sK0 @ (^[Y2 : sK0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ sK1 @ Y1 @ sK3) & ('const/sets/IN' @ sK0 @ Y2 @ sK2)) @ (X1 @ Y1 @ Y2)))))))))))) )),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f53])).
% 0.20/0.30 thf(f58,plain,(
% 0.20/0.30 ($true = $false)),
% 0.20/0.30 inference(backward_demodulation,[],[f29,f55])).
% 0.20/0.30 thf(f59,plain,(
% 0.20/0.30 $false),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f58])).
% 0.20/0.30 % SZS output end Proof for theBenchmark
% 0.20/0.30 % (258320)------------------------------
% 0.20/0.30 % (258320)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (258320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (258320)CaDiCaL version: 2.1.3
% 0.20/0.30 % (258320)Termination reason: Refutation
% 0.20/0.30 % (258320)Time elapsed: 0.009 s
% 0.20/0.30 % (258320)Peak memory usage: 12 MB
% 0.20/0.30 % (258320)Instructions burned: 13 (million)
% 0.20/0.30 % (258298)Success in time 0.069 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------