Higher-order Theorems Isabelle‑HOT
 2012
Isabelle
 2012
Satallax
 2.4
Satallax
 2.1
LEO‑II
 1.4.0
TPS
 3.120601S1b
Solved/200 166/200 135/200 132/200 123/200 81/200 66/200
Av. CPU Time 88.44 70.13 16.20 19.57 11.38 25.23
Solutions 0/200 0/200 0/200 0/200 80/200 0/200
μEfficiency 28 26 460 330 304 87
SOTAC 0.28 0.27 0.27 0.25 0.26 0.41
New Solved 12/13 12/13 13/13 11/13 12/13 0/13
Typed First-order Theorems +*-/ Princess
 120604
SPASS+T
 2.2.14
SPASS+T
 2.2.16
Solved/150 141/150 140/150 139/150
Av. CPU Time 10.22 6.45 4.65
Solutions 0/150 140/150 139/150
μEfficiency 393 797 797
SOTAC 0.36 0.34 0.34
New Solved 1/1 1/1 1/1
First-order Theorems Vampire
 2.6
E‑MaLeS
 1.1
EP
 1.6pre
Vampire
 0.6
EP
 1.4pre
iProver
 0.99
Prover9
 1109a
iProver‑Eq
 0.8
LEO‑II
 1.4.0
E‑KRHyper
 1.3
E‑Darwin
 1.5
Princess
 120604
SuperZenon
 0.0.1
Zenon
 0.7.1
STP
 1.0
Muscadet
 4.2
Solved/450 429/450 377/450 359/450 355/450 333/450 274/450 186/450 174/450 171/450 159/450 156/450 140/450 137/450 70/450 40/450 34/450
Av. CPU Time 13.17 17.85 13.46 11.81 18.98 17.76 17.70 21.11 19.11 31.86 16.11 55.47 4.15 13.29 10.70 15.43
Solutions 429/450 372/450 359/450 355/450 333/450 270/450 186/450 0/450 171/450 0/450 0/450 0/450 137/450 66/450 40/450 32/450
μEfficiency 614 562 509 516 428 326 238 238 197 217 220 22 251 102 53 54
SOTAC 0.18 0.14 0.14 0.14 0.13 0.13 0.11 0.10 0.11 0.11 0.10 0.11 0.14 0.09 0.13 0.12
New Solved 64/68 59/68 50/68 18/68 46/68 32/68 15/68 17/68 13/68 17/68 11/68 12/68 2/68 10/68 15/68 8/68
First-order Non-theorems Paradox
 3.0
Vampire‑SAT
 2.6
FIMO
 0.3
iProver‑SAT
 0.99
Nitrox
 2012
CVC4
 0.0
EP‑SAT
 1.6pre
E‑KRHyper
 1.3
E‑Darwin
 1.5
iProver‑Eq
 0.8
Solved/300 221/300 195/300 194/300 185/300 176/300 112/300 107/300 68/300 65/300 57/300
Av. CPU Time 6.45 13.81 15.70 49.96 23.53 25.55 3.87 5.29 14.00 17.30
Solutions 221/300 195/300 194/300 184/300 176/300 0/300 107/300 0/300 65/300 0/300
μEfficiency 600 410 400 167 50 225 286 146 163 91
SOTAC 0.27 0.22 0.20 0.23 0.22 0.16 0.26 0.17 0.15 0.14
New Solved 0/11 0/11 0/11 11/11 0/11 0/11 0/11 0/11 0/11 0/11
Effectively Propositional CNF iProver
 0.9
iProver
 0.99
Vampire‑EPR
 2.6
iProver‑Eq
 0.8
E‑Darwin
 1.5
EP
 1.6pre
CVC4
 0.0
E‑KRHyper
 1.3
Solved/150 140/150 138/150 111/150 77/150 67/150 52/150 50/150 49/150
Av. CPU Time 23.99 25.96 34.21 23.63 13.19 4.57 12.12 2.61
Solutions 64/150 73/150 109/150 0/150 60/150 52/150 0/150 0/150
μEfficiency 425 413 406 267 376 262 285 309
SOTAC 0.27 0.27 0.23 0.16 0.15 0.14 0.13 0.14
New Solved 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0
Large Theory Batch Problems Vampire‑LTB
 2.6
Vampire‑LTB
 1.8
EP‑LTB
 1.6pre
E‑MaLeS‑LTB
 1.1
iProver‑LTB
 0.99
iProver‑Eq‑LTB
 0.8
E‑KRHyper‑LTB
 1.3
leanCoP‑ARDE
 2.2
Solved/175 102/175 90/175 87/175 83/175 59/175 32/175 23/175 21/175
Av. CPU Time 20.68 21.40 67.44 43.67 30.05 20.44 2.99 34.26
Av. WC Time 5.02 5.05 9.44 10.80 10.96 10.25 3.01 9.90
Solutions 102/175 89/175 81/175 80/175 59/175 0/175 13/175 19/175
μEfficiency 133 115 89 61 33 18 27 17
SOTAC 0.29 0.25 0.23 0.24 0.21 0.16 0.16 0.16
Core Usage 3.37 4.47 7.92 7.21 5.58 3.72 1.00 4.68
New Solved 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0
THF without Equality Isabelle‑HOT
 2012
Satallax
 2.4
Satallax
 2.1
Isabelle
 2012
TPS
 3.120601S1b
LEO‑II
 1.4.0
Solved/50 34/50 31/50 29/50 19/50 18/50 7/50
Av. CPU Time 97.14 7.39 25.39 55.84 39.50 33.57
Solutions 0/50 0/50 0/50 0/50 0/50 7/50
μEfficiency 15 393 255 14 30 76
SOTAC 0.30 0.32 0.29 0.33 0.66 0.24
New Solved 0/0 0/0 0/0 0/0 0/0 0/0
THF with Equality Isabelle‑HOT
 2012
Isabelle
 2012
Satallax
 2.4
Satallax
 2.1
LEO‑II
 1.4.0
TPS
 3.120601S1b
Solved/150 132/150 116/150 101/150 94/150 74/150 48/150
Av. CPU Time 86.20 72.47 18.91 17.77 9.28 19.88
Solutions 0/150 0/150 0/150 0/150 73/150 0/150
μEfficiency 32 30 482 355 381 107
SOTAC 0.27 0.26 0.25 0.23 0.27 0.31
New Solved 12/13 12/13 13/13 11/13 12/13 0/13
TFA using Integers Princess
 120604
SPASS+T
 2.2.14
SPASS+T
 2.2.16
Solved/100 95/100 90/100 89/100
Av. CPU Time 13.62 9.92 7.14
Solutions 0/100 90/100 89/100
μEfficiency 418 696 696
SOTAC 0.37 0.34 0.33
New Solved 0/0 0/0 0/0
TFA using Rationals xor Reals SPASS+T
 2.2.14
SPASS+T
 2.2.16
Princess
 120604
Solved/50 50/50 50/50 46/50
Av. CPU Time 0.20 0.22 3.19
Solutions 50/50 50/50 0/50
μEfficiency 1000 1000 343
SOTAC 0.35 0.35 0.33
New Solved 1/1 1/1 1/1
FOF Theorems without Equality Vampire
 2.6
Vampire
 0.6
iProver
 0.99
E‑MaLeS
 1.1
EP
 1.6pre
iProver‑Eq
 0.8
LEO‑II
 1.4.0
EP
 1.4pre
E‑Darwin
 1.5
E‑KRHyper
 1.3
Zenon
 0.7.1
SuperZenon
 0.0.1
Princess
 120604
Prover9
 1109a
STP
 1.0
Muscadet
 4.2
Solved/100 99/100 96/100 92/100 90/100 90/100 89/100 85/100 84/100 70/100 55/100 48/100 45/100 42/100 39/100 14/100 11/100
Av. CPU Time 5.28 5.70 6.09 12.75 16.72 11.57 22.75 9.67 11.67 9.43 9.09 3.11 56.10 14.23 0.62 11.60
Solutions 99/100 96/100 92/100 89/100 90/100 0/100 85/100 84/100 0/100 0/100 45/100 45/100 0/100 39/100 14/100 11/100
μEfficiency 847 726 688 695 643 695 440 534 452 385 327 349 38 272 138 73
SOTAC 0.11 0.10 0.10 0.09 0.10 0.09 0.10 0.09 0.09 0.10 0.08 0.09 0.09 0.08 0.09 0.09
New Solved 13/13 13/13 13/13 12/13 9/13 13/13 9/13 9/13 9/13 3/13 8/13 0/13 10/13 11/13 13/13 4/13
FOF Theorems with Equality Vampire
 2.6
E‑MaLeS
 1.1
EP
 1.6pre
EP
 1.4pre
Vampire
 0.6
iProver
 0.99
LEO‑II
 1.4.0
Prover9
 1109a
Princess
 120604
E‑KRHyper
 1.3
E‑Darwin
 1.5
iProver‑Eq
 0.8
SuperZenon
 0.0.1
Muscadet
 4.2
Zenon
 0.7.1
STP
 1.0
Solved/200 191/200 161/200 144/200 127/200 125/200 89/200 76/200 54/200 54/200 50/200 43/200 32/200 30/200 23/200 15/200 14/200
Av. CPU Time 17.93 21.29 8.75 26.98 16.72 25.69 15.64 12.01 58.91 49.78 12.95 35.42 3.57 17.26 29.01 25.24
Solutions 191/200 160/200 144/200 127/200 125/200 85/200 76/200 54/200 0/200 0/200 0/200 0/200 30/200 21/200 15/200 14/200
μEfficiency 465 453 395 275 362 152 179 138 18 132 149 67 122 86 49 23
SOTAC 0.23 0.18 0.17 0.15 0.17 0.15 0.12 0.13 0.11 0.11 0.10 0.10 0.13 0.14 0.10 0.19
New Solved 51/55 47/55 41/55 37/55 5/55 19/55 4/55 4/55 2/55 14/55 2/55 4/55 2/55 4/55 2/55 2/55
Unsatisfiable CNF without Equality Vampire
 2.6
Vampire
 0.6
E‑MaLeS
 1.1
EP
 1.6pre
EP
 1.4pre
iProver
 0.99
iProver‑Eq
 0.8
Prover9
 1109a
E‑KRHyper
 1.3
E‑Darwin
 1.5
SuperZenon
 0.0.1
STP
 1.0
LEO‑II
 1.4.0
Princess
 120604
Zenon
 0.7.1
Muscadet
 4.2
Solved/50 49/50 45/50 44/50 42/50 41/50 38/50 36/50 34/50 18/50 13/50 9/50 6/50 5/50 5/50 1/50 0/50
Av. CPU Time 19.04 22.41 26.82 20.31 16.48 19.06 10.23 40.42 50.36 58.93 0.06 1.79 29.16 47.45 39.83 -
Solutions 49/50 45/50 42/50 42/50 41/50 38/50 0/50 34/50 0/50 0/50 9/50 6/50 5/50 0/50 0/50 0/50
μEfficiency 587 491 554 502 471 399 410 292 173 120 180 87 80 10 1 -
SOTAC 0.16 0.15 0.13 0.13 0.13 0.13 0.12 0.12 0.11 0.11 0.14 0.10 0.10 0.11 0.10 -
New Solved 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0
Unsatisfiable CNF with Equality Vampire
 2.6
Vampire
 0.6
EP
 1.6pre
E‑MaLeS
 1.1
EP
 1.4pre
Prover9
 1109a
iProver
 0.99
SuperZenon
 0.0.1
Princess
 120604
E‑KRHyper
 1.3
E‑Darwin
 1.5
iProver‑Eq
 0.8
Zenon
 0.7.1
STP
 1.0
LEO‑II
 1.4.0
Muscadet
 4.2
Solved/100 90/100 89/100 83/100 82/100 81/100 59/100 55/100 53/100 39/100 36/100 30/100 17/100 6/100 6/100 5/100 0/100
Av. CPU Time 8.57 6.14 14.62 11.89 17.35 12.12 23.56 6.05 51.06 31.99 12.42 67.14 3.15 9.17 0.07 -
Solutions 90/100 89/100 83/100 81/100 81/100 59/100 55/100 53/100 0/100 0/100 0/100 0/100 6/100 6/100 5/100 0/100
μEfficiency 694 625 608 651 604 379 275 445 19 243 182 36 33 12 50 -
SOTAC 0.15 0.14 0.13 0.13 0.13 0.12 0.13 0.20 0.13 0.11 0.10 0.09 0.09 0.08 0.15 -
New Solved 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0
FOF Non-theorems without Equality iProver‑SAT
 0.99
Paradox
 3.0
FIMO
 0.3
Nitrox
 2012
Vampire‑SAT
 2.6
EP‑SAT
 1.6pre
iProver‑Eq
 0.8
CVC4
 0.0
E‑KRHyper
 1.3
E‑Darwin
 1.5
Solved/50 38/50 34/50 32/50 31/50 26/50 23/50 21/50 16/50 12/50 11/50
Av. CPU Time 37.01 5.64 43.13 19.84 8.73 4.65 26.40 16.63 2.81 4.72
Solutions 38/50 34/50 32/50 31/50 26/50 23/50 0/50 0/50 0/50 11/50
μEfficiency 275 485 277 43 216 214 199 214 189 160
SOTAC 0.40 0.18 0.17 0.17 0.15 0.24 0.14 0.15 0.14 0.12
New Solved 11/11 0/11 0/11 0/11 0/11 0/11 0/11 0/11 0/11 0/11
FOF Non-theorems with Equality iProver‑SAT
 0.99
Vampire‑SAT
 2.6
FIMO
 0.3
Paradox
 3.0
EP‑SAT
 1.6pre
E‑KRHyper
 1.3
Nitrox
 2012
CVC4
 0.0
E‑Darwin
 1.5
iProver‑Eq
 0.8
Solved/100 79/100 78/100 77/100 63/100 55/100 53/100 49/100 36/100 34/100 15/100
Av. CPU Time 62.03 26.64 9.24 0.38 0.88 5.83 32.85 48.44 24.88 14.86
Solutions 79/100 78/100 77/100 63/100 55/100 0/100 49/100 0/100 34/100 0/100
μEfficiency 84 464 440 604 499 322 38 152 234 53
SOTAC 0.21 0.18 0.20 0.18 0.18 0.18 0.20 0.16 0.16 0.12
New Solved 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0
Satisfiable CNF without Equality Paradox
 3.0
Nitrox
 2012
FIMO
 0.3
Vampire‑SAT
 2.6
iProver‑SAT
 0.99
CVC4
 0.0
iProver‑Eq
 0.8
E‑Darwin
 1.5
EP‑SAT
 1.6pre
E‑KRHyper
 1.3
Solved/50 50/50 49/50 35/50 34/50 32/50 30/50 17/50 14/50 2/50 1/50
Av. CPU Time 1.97 16.46 1.78 2.97 32.48 5.16 11.00 0.18 0.01 0.00
Solutions 50/50 49/50 35/50 34/50 32/50 0/50 0/50 14/50 2/50 0/50
μEfficiency 853 78 625 574 351 395 198 280 40 20
SOTAC 0.26 0.25 0.16 0.16 0.15 0.15 0.13 0.13 0.11 0.10
New Solved 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0
Satisfiable CNF with Equality Paradox
 3.0
Vampire‑SAT
 2.6
FIMO
 0.3
Nitrox
 2012
iProver‑SAT
 0.99
CVC4
 0.0
EP‑SAT
 1.6pre
E‑Darwin
 1.5
iProver‑Eq
 0.8
E‑KRHyper
 1.3
Solved/100 74/100 57/100 50/100 47/100 36/100 30/100 27/100 6/100 4/100 2/100
Av. CPU Time 15.03 5.03 17.82 23.61 52.66 23.23 9.59 1.65 5.45 8.37
Solutions 74/100 57/100 50/100 47/100 35/100 0/100 27/100 6/100 0/100 0/100
μEfficiency 526 373 310 53 104 218 233 36 22 11
SOTAC 0.40 0.35 0.26 0.24 0.19 0.19 0.45 0.18 0.16 0.16
New Solved 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0
EPR Unsatisfiable CNF iProver
 0.9
iProver
 0.99
Vampire‑EPR
 2.6
iProver‑Eq
 0.8
E‑Darwin
 1.5
EP
 1.6pre
E‑KRHyper
 1.3
CVC4
 0.0
Solved/75 68/75 66/75 43/75 11/75 7/75 1/75 1/75 0/75
Av. CPU Time 45.99 50.33 75.80 97.71 56.85 0.08 81.70 -
Solutions 0/75 3/75 43/75 0/75 0/75 1/75 0/75 0/75
μEfficiency 54 42 38 15 18 13 0 -
SOTAC 0.39 0.39 0.36 0.24 0.22 0.17 0.50 -
New Solved 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0
EPR Satisfiable CNF iProver
 0.9
iProver
 0.99
Vampire‑EPR
 2.6
iProver‑Eq
 0.8
E‑Darwin
 1.5
EP
 1.6pre
CVC4
 0.0
E‑KRHyper
 1.3
Solved/75 72/75 72/75 68/75 66/75 60/75 51/75 50/75 48/75
Av. CPU Time 3.20 3.62 7.91 11.28 8.10 4.66 12.12 0.96
Solutions 64/75 70/75 66/75 0/75 60/75 51/75 0/75 0/75
μEfficiency 796 784 774 518 734 510 571 617
SOTAC 0.16 0.16 0.15 0.15 0.15 0.14 0.13 0.13
New Solved 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0
LTB Isabelle Theorems Vampire‑LTB
 2.6
E‑MaLeS‑LTB
 1.1
EP‑LTB
 1.6pre
Vampire‑LTB
 1.8
iProver‑LTB
 0.99
leanCoP‑ARDE
 2.2
iProver‑Eq‑LTB
 0.8
E‑KRHyper‑LTB
 1.3
Solved/75 54/75 50/75 47/75 39/75 25/75 17/75 16/75 7/75
Av. CPU Time 28.63 47.19 86.60 20.55 34.65 41.09 14.77 3.83
Av. WC Time 6.13 11.55 11.39 4.63 11.31 11.87 9.40 3.88
Solutions 54/75 49/75 42/75 39/75 25/75 17/75 0/75 0/75
μEfficiency 155 86 101 133 34 26 19 16
SOTAC 0.27 0.26 0.25 0.22 0.18 0.16 0.16 0.13
Core Usage 5.39 5.30 7.89 4.47 5.58 4.68 3.42 0.99
New Solved 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0
LTB Mizar Theorems Vampire‑LTB
 2.6
Vampire‑LTB
 1.8
EP‑LTB
 1.6pre
E‑MaLeS‑LTB
 1.1
iProver‑LTB
 0.99
iProver‑Eq‑LTB
 0.8
E‑KRHyper‑LTB
 1.3
leanCoP‑ARDE
 2.2
Solved/80 36/80 33/80 25/80 22/80 18/80 6/80 3/80 2/80
Av. CPU Time 12.09 27.27 54.70 49.38 26.56 25.71 0.00 7.82
Av. WC Time 3.26 6.20 7.82 10.39 11.03 11.53 0.00 1.50
Solutions 36/80 33/80 24/80 20/80 18/80 0/80 0/80 2/80
μEfficiency 106 83 66 41 23 8 12 6
SOTAC 0.34 0.28 0.24 0.23 0.26 0.17 0.16 0.13
Core Usage 5.44 5.32 7.92 7.21 5.36 3.72 5.20
New Solved 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0
LTB SUMO Questions Vampire‑LTB
 1.8
iProver‑LTB
 0.99
EP‑LTB
 1.6pre
E‑KRHyper‑LTB
 1.3
Vampire‑LTB
 2.6
E‑MaLeS‑LTB
 1.1
iProver‑Eq‑LTB
 0.8
leanCoP‑ARDE
 2.2
Solved/20 18/20 16/20 15/20 13/20 12/20 11/20 10/20 2/20
Av. CPU Time 12.47 26.78 28.65 3.22 10.63 16.23 26.36 2.58
Av. WC Time 3.85 10.34 6.02 3.24 5.26 8.20 10.83 1.50
Answers 17/20 16/20 15/20 13/20 12/20 11/20 0/20 0/20
μEfficiency 177 72 139 128 159 52 52 25
SOTAC 0.27 0.20 0.18 0.17 0.21 0.16 0.15 0.12
Core Usage 5.21 5.25 3.94 1.00 2.35 3.81 3.81 1.72
New Solved 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0